(herald nhca (algebra diffie-hellman) (bound 20))

(comment "CPSA 3.6.7")
(comment "All input read from tst/nh-ca-w-dh.scm")
(comment "Strand count bounded at 20")

(defprotocol nhca diffie-hellman
  (defrole init
    (vars (xi rndx) (xr expt) (a b ca name) (n text) (hint mesg))
    (trace (send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    (non-orig (privk a) (privk ca))
    (uniq-gen xi))
  (defrole resp
    (vars (xr rndx) (xi expt) (a b ca name) (n text))
    (trace (send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    (non-orig (privk b) (privk ca))
    (uniq-gen xr))
  (defrole ca
    (vars (subject ca name) (x expt))
    (trace (recv (enc "reg" (exp (gen) x) subject (privk subject)))
      (send (enc (exp (gen) x) subject (privk ca))))
    (non-orig (privk subject)))
  (comment A diffie-hellman exchange which uses a certificate authority
    to certify lonh-term NH values))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (comment Full initiator POV No need to make extra assumptions)
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint))))))
  (label 0)
  (unrealized (0 1) (0 3))
  (origs)
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 1)
  (parent 0)
  (unrealized (0 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a ca name) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test (displaced 2 1 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi) hint (enc (exp (gen) xi) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 2)
  (parent 1)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr x))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((2 1) (0 3)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi x)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi x)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi x)) x)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 3)
  (parent 1)
  (unrealized (0 3) (2 0))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a ca name) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((1 1) (0 1)) ((2 1) (0 3)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi) hint (enc (exp (gen) xi) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))))
  (label 4)
  (parent 2)
  (unrealized (2 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a ca name) (xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((1 1) (0 1)) ((2 1) (0 3)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xr)
  (operation encryption-test (displaced 3 0 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (send (cat (exp (gen) xr) (enc (exp (gen) xr) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca)))))
  (label 5)
  (parent 3)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 1 (b b) (xr xr))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((2 1) (0 3)) ((3 0) (2 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr) b (privk b)) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))))
  (label 6)
  (parent 3)
  (unrealized (0 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a ca name) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (precedes ((0 0) (1 0)) ((0 0) (3 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 1) (2 0)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi) hint (enc (exp (gen) xi) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))))
  (label 7)
  (parent 4)
  (unrealized (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a ca name) (xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (3 0)) ((1 1) (0 1))
    ((2 1) (0 3)) ((3 1) (0 3)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xr)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (send (cat (exp (gen) xr) (enc (exp (gen) xr) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))))
  (label 8)
  (parent 5)
  (unrealized (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (a ca a-0 b ca-0 name) (xi xr rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca-0) (xr xr) (xi xi))
  (precedes ((0 0) (1 0)) ((0 0) (3 2)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 3) (0 3)))
  (non-orig (privk a) (privk ca) (privk b) (privk ca-0))
  (uniq-gen xi xr)
  (operation encryption-test (displaced 3 4 resp 4)
    (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
      (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
        (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr)))) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca-0)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca-0))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))))
  (label 9)
  (parent 6)
  (unrealized (3 1) (3 2))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 1 (b b) (xr xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((4 1) (0 3)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))))
  (label 10)
  (parent 6)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a ca name) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi)) xi))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 1) (2 0)) ((4 1) (3 0)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi)) xi))
    (hash "share" (exp (gen) (mul xi xi)) xi) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi) hint (enc (exp (gen) xi) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi)) xi))
      (send (cat "share" (exp (gen) (mul xi xi)) xi))))
  (label 11)
  (parent 7)
  (unrealized (4 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a ca name) (xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (4 0)) ((1 1) (0 1))
    ((2 1) (0 3)) ((3 1) (0 3)) ((4 1) (3 0)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xr)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (send (cat (exp (gen) xr) (enc (exp (gen) xr) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))))
  (label 12)
  (parent 8)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (a ca a-0 b name) (xi xr rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca) (xr xr) (xi xi))
  (precedes ((0 0) (1 0)) ((0 0) (3 2)) ((1 1) (0 1)) ((2 1) (3 1))
    ((3 0) (2 0)) ((3 3) (0 3)))
  (non-orig (privk a) (privk ca) (privk b))
  (uniq-gen xi xr)
  (operation encryption-test (displaced 4 2 ca 2)
    (enc (exp (gen) xr) b (privk ca-0)) (3 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))))
  (label 13)
  (parent 9)
  (unrealized (3 2))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (n text) (a ca a-0 b ca-0 name) (xi xr rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca-0) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (3 2)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 3) (0 3)) ((4 1) (3 1)))
  (non-orig (privk a) (privk ca) (privk b) (privk ca-0))
  (uniq-gen xi xr)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr) b (privk ca-0)) (3 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca-0)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca-0))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0)))))
  (label 14)
  (parent 9)
  (unrealized (3 2))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 1 (b b) (xr xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (5 0)) ((4 1) (0 3)) ((5 1) (4 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))))
  (label 15)
  (parent 10)
  (unrealized (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a ca name) (xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (deflistener (cat "share" (exp (gen) (mul xr xr)) xr))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (5 0)) ((1 1) (0 1))
    ((2 1) (0 3)) ((3 1) (0 3)) ((4 1) (3 0)) ((5 1) (4 0)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xr)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr xr)) xr))
    (hash "share" (exp (gen) (mul xr xr)) xr) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (send (cat (exp (gen) xr) (enc (exp (gen) xr) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint)))
    ((recv (cat "share" (exp (gen) (mul xr xr)) xr))
      (send (cat "share" (exp (gen) (mul xr xr)) xr))))
  (label 16)
  (parent 12)
  (unrealized (5 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (n text) (a ca b name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((1 1) (3 2)) ((2 1) (3 1))
    ((3 0) (2 0)) ((3 3) (0 3)))
  (non-orig (privk a) (privk ca) (privk b))
  (uniq-gen xr xi)
  (operation encryption-test (displaced 4 1 ca 2)
    (enc (exp (gen) xi) a-0 (privk ca)) (3 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))))
  (label 17)
  (parent 13)
  (unrealized)
  (shape)
  (maps
    ((0)
      ((xi xi) (xr xr) (a a) (b b) (ca ca) (n n)
        (hint
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
  (origs))

(defskeleton nhca
  (vars (n text) (a ca a-0 b name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a-0) (ca ca) (x xi))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (3 1))
    ((3 0) (2 0)) ((3 3) (0 3)) ((4 1) (3 2)))
  (non-orig (privk a) (privk ca) (privk a-0) (privk b))
  (uniq-gen xr xi)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a-0 (privk ca)) (3 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a-0 (privk a-0)))
      (send (enc (exp (gen) xi) a-0 (privk ca)))))
  (label 18)
  (parent 13)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (a ca b name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((1 1) (3 2)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 3) (0 3)) ((4 1) (3 1)))
  (non-orig (privk a) (privk ca) (privk b))
  (uniq-gen xr xi)
  (operation encryption-test (displaced 5 1 ca 2)
    (enc (exp (gen) xi) a-0 (privk ca-0)) (3 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 19)
  (parent 14)
  (seen 17)
  (unrealized)
  (comment "1 in cohort - 0 not yet seen"))

(defskeleton nhca
  (vars (n text) (a ca a-0 b ca-0 name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca-0) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a-0) (ca ca-0) (x xi))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 3) (0 3)) ((4 1) (3 1))
    ((5 1) (3 2)))
  (non-orig (privk a) (privk ca) (privk a-0) (privk b) (privk ca-0))
  (uniq-gen xr xi)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a-0 (privk ca-0)) (3 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca-0)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca-0))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a-0 (privk a-0)))
      (send (enc (exp (gen) xi) a-0 (privk ca-0)))))
  (label 20)
  (parent 14)
  (unrealized (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 1 (b b) (xr xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr)) xi))
  (precedes ((0 0) (1 0)) ((0 0) (6 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (6 0)) ((4 1) (0 3)) ((5 1) (4 0))
    ((6 1) (5 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr)) xi))
    (hash "share" (exp (gen) (mul xi xr)) xi) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr)) xi))
      (send (cat "share" (exp (gen) (mul xi xr)) xi))))
  (label 21)
  (parent 15)
  (unrealized (6 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (n text) (a ca b name) (xr xr-0 rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b b) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (3 1))
    ((3 0) (2 0)) ((3 3) (0 3)) ((4 1) (3 2)))
  (non-orig (privk a) (privk ca) (privk b))
  (uniq-gen xr xr-0)
  (operation encryption-test (displaced 5 0 resp 1)
    (enc "reg" (exp (gen) xr-0) a-0 (privk a-0)) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 22)
  (parent 18)
  (unrealized)
  (shape)
  (maps
    ((0)
      ((xi xr-0) (xr xr) (a a) (b b) (ca ca) (n n)
        (hint
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
  (origs))

(defskeleton nhca
  (vars (n text) (a ca b ca-0 name) (xr xr-0 rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b b) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a) (b b) (ca ca-0) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 3) (0 3)) ((4 1) (3 1))
    ((5 1) (3 2)))
  (non-orig (privk a) (privk ca) (privk b) (privk ca-0))
  (uniq-gen xr xr-0)
  (operation encryption-test (displaced 6 0 resp 1)
    (enc "reg" (exp (gen) xr-0) a-0 (privk a-0)) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca-0)))
      (recv
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0)))))
  (label 23)
  (parent 20)
  (unrealized)
  (shape)
  (maps
    ((0)
      ((xi xr-0) (xr xr) (a a) (b b) (ca ca) (n n)
        (hint
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
  (origs))

(comment "Nothing left to do")

(defprotocol nhca diffie-hellman
  (defrole init
    (vars (xi rndx) (xr expt) (a b ca name) (n text) (hint mesg))
    (trace (send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    (non-orig (privk a) (privk ca))
    (uniq-gen xi))
  (defrole resp
    (vars (xr rndx) (xi expt) (a b ca name) (n text))
    (trace (send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    (non-orig (privk b) (privk ca))
    (uniq-gen xr))
  (defrole ca
    (vars (subject ca name) (x expt))
    (trace (recv (enc "reg" (exp (gen) x) subject (privk subject)))
      (send (enc (exp (gen) x) subject (privk ca))))
    (non-orig (privk subject)))
  (comment A diffie-hellman exchange which uses a certificate authority
    to certify lonh-term NH values))

(defskeleton nhca
  (vars (n text) (a b ca name) (xr rndx) (xi expt))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (comment Full responder point of view with freshly chosen n)
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr)))))))
  (label 24)
  (unrealized (0 1) (0 2) (0 4))
  (origs (n (0 3)))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (a b ca name) (xi expt) (xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr) b (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 25)
  (parent 24)
  (unrealized (0 2) (0 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test (displaced 2 1 ca 2)
    (enc (exp (gen) x) a (privk ca)) (0 2))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 26)
  (parent 25)
  (unrealized (0 4))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (a b ca name) (xr rndx) (x expt))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi x))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x x))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((2 1) (0 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) a (privk ca)) (0 2))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) x) (enc (exp (gen) x) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr x)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr x)) x)
              (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr x)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) x) a (privk a)))
      (send (enc (exp (gen) x) a (privk ca)))))
  (label 27)
  (parent 25)
  (unrealized (0 4) (2 0))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((1 1) (0 1)) ((2 1) (0 4)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))) (0 4))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
  (label 28)
  (parent 26)
  (unrealized (2 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((1 1) (0 1)) ((2 1) (0 2)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test (displaced 3 0 resp 1)
    (enc "reg" (exp (gen) xr-0) a (privk a)) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 29)
  (parent 27)
  (unrealized (0 4))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (a b ca name) (xr xr-0 rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand resp 1 (b a) (xr xr-0))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((2 1) (0 2)) ((3 0) (2 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) a (privk a)) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))))
  (label 30)
  (parent 27)
  (unrealized (0 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (3 0)) ((1 1) (0 1)) ((2 1) (0 4))
    ((3 1) (2 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
  (label 31)
  (parent 28)
  (unrealized (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (3 0)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 1) (0 4)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))) (0 4))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
  (label 32)
  (parent 29)
  (unrealized (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca a b-0 ca-0 name) (xr xi rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b-0) (ca ca-0) (xi xi) (xr xr))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 4) (0 4)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (displaced 3 4 init 5)
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr)))) (0 4))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b-0 (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))))
  (label 33)
  (parent 30)
  (unrealized (3 1) (3 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (n text) (a b ca name) (xr xr-0 rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand resp 1 (b a) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (4 0)) ((4 1) (0 4)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
    (0 4))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
  (label 34)
  (parent 30)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener (cat "share" (exp (gen) (mul xr xr)) xr))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (0 4))
    ((3 1) (2 0)) ((4 1) (3 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr xr)) xr))
    (hash "share" (exp (gen) (mul xr xr)) xr) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv (cat "share" (exp (gen) (mul xr xr)) xr))
      (send (cat "share" (exp (gen) (mul xr xr)) xr))))
  (label 35)
  (parent 31)
  (unrealized (4 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (4 0)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 1) (0 4)) ((4 1) (3 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
  (label 36)
  (parent 32)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca a b-0 name) (xr xi rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b-0) (ca ca) (xi xi) (xr xr))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((2 1) (3 1)) ((3 0) (2 0)) ((3 4) (0 4)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (displaced 4 2 ca 2)
    (enc (exp (gen) xi) a (privk ca-0)) (3 1))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b-0 (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))))
  (label 37)
  (parent 33)
  (unrealized (3 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca a b-0 ca-0 name) (xr xi rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b-0) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 4) (0 4)) ((4 1) (3 1)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a (privk ca-0)) (3 1))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b-0 (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0)))))
  (label 38)
  (parent 33)
  (unrealized (3 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (n text) (a b ca name) (xr xr-0 rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand resp 1 (b a) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (5 0)) ((4 1) (0 4)) ((5 1) (4 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
    (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
  (label 39)
  (parent 34)
  (unrealized (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener (cat "share" (exp (gen) (mul xr xr)) xr))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (5 0)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 1) (0 4)) ((4 1) (3 0)) ((5 1) (4 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr xr)) xr))
    (hash "share" (exp (gen) (mul xr xr)) xr) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv (cat "share" (exp (gen) (mul xr xr)) xr))
      (send (cat "share" (exp (gen) (mul xr xr)) xr))))
  (label 40)
  (parent 36)
  (unrealized (5 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (n text) (b ca a name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((2 1) (3 1)) ((3 0) (2 0)) ((3 4) (0 4)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 4 1 ca 2)
    (enc (exp (gen) xr) b-0 (privk ca)) (3 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))))
  (label 41)
  (parent 37)
  (unrealized)
  (shape)
  (maps ((0) ((n n) (xr xr) (xi xi) (a a) (b b) (ca ca))))
  (origs (n (0 3))))

(defskeleton nhca
  (vars (n text) (b ca a b-0 name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b-0) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b-0) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((0 3) (3 3)) ((1 1) (0 1))
    ((2 1) (0 2)) ((2 1) (3 1)) ((3 0) (2 0)) ((3 4) (0 4))
    ((4 1) (3 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk b-0))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr) b-0 (privk ca)) (3 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b-0 (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b-0 (privk b-0)))
      (send (enc (exp (gen) xr) b-0 (privk ca)))))
  (label 42)
  (parent 37)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca a name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 4) (0 4)) ((4 1) (3 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 5 1 ca 2)
    (enc (exp (gen) xr) b-0 (privk ca-0)) (3 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 43)
  (parent 38)
  (unrealized)
  (shape)
  (maps ((0) ((n n) (xr xr) (xi xi) (a a) (b b) (ca ca))))
  (origs (n (0 3))))

(defskeleton nhca
  (vars (n text) (b ca a b-0 ca-0 name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b-0) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b-0) (ca ca-0) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((0 3) (3 3)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 0) (2 0)) ((3 0) (4 0)) ((3 4) (0 4))
    ((4 1) (3 1)) ((5 1) (3 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk b-0) (privk ca-0))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr) b-0 (privk ca-0)) (3 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b-0 (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b-0 (privk b-0)))
      (send (enc (exp (gen) xr) b-0 (privk ca-0)))))
  (label 44)
  (parent 38)
  (unrealized (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (a b ca name) (xr xr-0 rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand resp 1 (b a) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (deflistener (cat "share" (exp (gen) (mul xr xr-0)) xr))
  (precedes ((0 0) (1 0)) ((0 0) (6 0)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (6 0)) ((4 1) (0 4)) ((5 1) (4 0))
    ((6 1) (5 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr xr-0)) xr))
    (hash "share" (exp (gen) (mul xr xr-0)) xr) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))))
    ((recv (cat "share" (exp (gen) (mul xr xr-0)) xr))
      (send (cat "share" (exp (gen) (mul xr xr-0)) xr))))
  (label 45)
  (parent 39)
  (unrealized (6 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (n text) (b ca a name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((0 3) (3 3)) ((1 1) (0 1))
    ((2 1) (0 2)) ((2 1) (3 1)) ((3 0) (2 0)) ((3 4) (0 4))
    ((4 1) (3 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 5 0 resp 1)
    (enc "reg" (exp (gen) xr) b-0 (privk b-0)) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 46)
  (parent 42)
  (seen 41)
  (unrealized)
  (comment "1 in cohort - 0 not yet seen"))

(defskeleton nhca
  (vars (n text) (b ca a ca-0 name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((0 3) (3 3)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 0) (2 0)) ((3 0) (4 0)) ((3 4) (0 4))
    ((4 1) (3 1)) ((5 1) (3 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 6 0 resp 1)
    (enc "reg" (exp (gen) xr) b-0 (privk b-0)) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0)))))
  (label 47)
  (parent 44)
  (unrealized)
  (shape)
  (maps ((0) ((n n) (xr xr) (xi xi) (a a) (b b) (ca ca))))
  (origs (n (0 3))))

(comment "Nothing left to do")

(defprotocol nhca diffie-hellman
  (defrole init
    (vars (xi rndx) (xr expt) (a b ca name) (n text) (hint mesg))
    (trace (send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    (non-orig (privk a) (privk ca))
    (uniq-gen xi))
  (defrole resp
    (vars (xr rndx) (xi expt) (a b ca name) (n text))
    (trace (send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    (non-orig (privk b) (privk ca))
    (uniq-gen xr))
  (defrole ca
    (vars (subject ca name) (x expt))
    (trace (recv (enc "reg" (exp (gen) x) subject (privk subject)))
      (send (enc (exp (gen) x) subject (privk ca))))
    (non-orig (privk subject)))
  (comment A diffie-hellman exchange which uses a certificate authority
    to certify lonh-term NH values))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx)
    (xr-0 xi-0 expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi-0))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (uniq-orig n)
  (comment point of view in which init and resp each complete and they
    agree on the relevant parameters)
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
  (label 48)
  (unrealized (0 1) (0 3) (1 1) (1 2) (1 4))
  (preskeleton)
  (origs (n (1 3)))
  (comment "Not a skeleton"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx)
    (xr-0 xi-0 expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi-0))
  (precedes ((1 3) (0 3)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (uniq-orig n)
  (comment point of view in which init and resp each complete and they
    agree on the relevant parameters)
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
  (label 49)
  (parent 48)
  (unrealized (0 1) (0 3) (1 1) (1 2) (1 4))
  (origs (n (1 3)))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr xi-0 expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr-0) b (privk ca)) (1 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca)))))
  (label 50)
  (parent 49)
  (unrealized (0 1) (0 3) (1 2) (1 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 3 2 ca 2)
    (enc (exp (gen) x) a (privk ca)) (1 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca)))))
  (label 51)
  (parent 50)
  (unrealized (0 1) (0 3) (1 4))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi x))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x x))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) a (privk ca)) (1 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) x) (enc (exp (gen) x) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 x)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr-0 x)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 x)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 x)) xr-0))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr-0 x)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 x)) x)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 x)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 x)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 x)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) x) a (privk a)))
      (send (enc (exp (gen) x) a (privk ca)))))
  (label 52)
  (parent 50)
  (unrealized (0 1) (0 3) (1 4) (3 0))
  (comment "3 in cohort - 3 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 4)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
  (label 53)
  (parent 51)
  (unrealized (0 1) (0 3) (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xr-1)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (precedes ((0 0) (3 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test (displaced 4 0 resp 1)
    (enc "reg" (exp (gen) xr-2) a (privk a)) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))
      (recv (enc (exp (gen) xr-1) a (privk ca)))
      (send (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca)))))
  (label 54)
  (parent 52)
  (unrealized (0 1) (0 3) (1 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 4 1 resp 1)
    (enc "reg" (exp (gen) xr-1) a (privk a)) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca)))))
  (label 55)
  (parent 52)
  (unrealized (0 1) (0 3) (1 4))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (defstrand resp 1 (b a) (xr xr-1))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-1) a (privk a)) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))))
  (label 56)
  (parent 52)
  (unrealized (0 1) (0 3) (1 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (4 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 4)) ((4 1) (3 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))
    (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
  (label 57)
  (parent 53)
  (unrealized (0 1) (0 3) (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (3 0)) ((0 4) (1 4)) ((1 0) (2 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (1 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 4 0 init 5)
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xi)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 58)
  (parent 54)
  (unrealized (0 1))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xr-1)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (precedes ((0 0) (3 0)) ((0 0) (4 0)) ((1 0) (2 0)) ((1 0) (4 0))
    ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))
      (recv (enc (exp (gen) xr-1) a (privk ca)))
      (send (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
  (label 59)
  (parent 54)
  (unrealized (0 1) (0 3) (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 0) (4 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
  (label 60)
  (parent 55)
  (unrealized (0 1) (0 3) (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a b-0 ca-0 name) (xi rndx) (xr expt)
    (xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca-0) (xi xi-0) (xr xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 4) (1 4)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 4 5 init 5)
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca-0))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))))
  (label 61)
  (parent 56)
  (unrealized (0 1) (0 3) (4 1) (4 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (defstrand resp 1 (b a) (xr xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((5 1) (1 4)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-1) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
  (label 62)
  (parent 56)
  (unrealized (0 1) (0 3) (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 4)) ((4 1) (3 0)) ((5 1) (4 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 63)
  (parent 57)
  (unrealized (0 1) (0 3) (5 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (n text) (a b ca name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (3 0)) ((0 4) (1 4)) ((1 0) (2 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (0 1)) ((3 1) (1 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (displaced 4 3 ca 2)
    (enc (exp (gen) xi) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 64)
  (parent 58)
  (unrealized)
  (shape)
  (maps
    ((0 1)
      ((a a) (b b) (ca ca) (xi xi) (xr xr) (n n) (xr-0 xr)
        (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr)))
        (xi-0 xi))))
  (origs (n (1 3))))

(defskeleton nhca
  (vars (n text) (a b ca name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (3 0)) ((0 0) (4 0)) ((0 4) (1 4)) ((1 0) (2 0))
    ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (0 1)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 65)
  (parent 58)
  (unrealized)
  (shape)
  (maps
    ((0 1)
      ((a a) (b b) (ca ca) (xi xi) (xr xr) (n n) (xr-0 xr)
        (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr)))
        (xi-0 xi))))
  (origs (n (1 3))))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xr-1)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (precedes ((0 0) (3 0)) ((0 0) (5 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4))
    ((5 1) (4 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))
    (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))
      (recv (enc (exp (gen) xr-1) a (privk ca)))
      (send (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
  (label 66)
  (parent 59)
  (unrealized (0 1) (0 3) (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4)) ((5 1) (4 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))
    (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
  (label 67)
  (parent 60)
  (unrealized (0 1) (0 3) (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a b-0 name) (xi rndx) (xr expt)
    (xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca) (xi xi-0) (xr xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 5 3 ca 2)
    (enc (exp (gen) xi-0) a (privk ca-0)) (4 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))))
  (label 68)
  (parent 61)
  (unrealized (0 1) (0 3) (4 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a b-0 ca-0 name) (xi rndx) (xr expt)
    (xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca-0) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca-0)) (4 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca-0))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0)))))
  (label 69)
  (parent 61)
  (unrealized (0 1) (0 3) (4 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (defstrand resp 1 (b a) (xr xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (6 0)) ((5 1) (1 4))
    ((6 1) (5 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))
    (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-1) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
  (label 70)
  (parent 62)
  (unrealized (0 1) (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xr-1)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
  (precedes ((0 0) (3 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4))
    ((5 1) (4 0)) ((6 1) (5 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))
      (recv (enc (exp (gen) xr-1) a (privk ca)))
      (send (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (label 71)
  (parent 66)
  (unrealized (0 1) (0 3) (6 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4)) ((5 1) (4 0))
    ((6 1) (5 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 72)
  (parent 67)
  (unrealized (0 1) (0 3) (6 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi-0) (xr xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 5 2 ca 2)
    (enc (exp (gen) xr-0) b-0 (privk ca)) (4 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))))
  (label 73)
  (parent 68)
  (unrealized (0 1) (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a b-0 name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject b-0) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk b-0))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr-0) b-0 (privk ca)) (4 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xr-0) b-0 (privk b-0)))
      (send (enc (exp (gen) xr-0) b-0 (privk ca)))))
  (label 74)
  (parent 68)
  (unrealized (0 1) (0 3) (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 6 2 ca 2)
    (enc (exp (gen) xr-0) b-0 (privk ca-0)) (4 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 75)
  (parent 69)
  (unrealized (0 1) (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a b-0 ca-0 name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca-0) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject b-0) (ca ca-0) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk b-0) (privk ca-0))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr-0) b-0 (privk ca-0)) (4 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca-0))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) b-0 (privk b-0)))
      (send (enc (exp (gen) xr-0) b-0 (privk ca-0)))))
  (label 76)
  (parent 69)
  (unrealized (0 1) (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (defstrand resp 1 (b a) (xr xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (7 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (7 0)) ((5 1) (1 4))
    ((6 1) (5 0)) ((7 1) (6 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-1) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (label 77)
  (parent 70)
  (unrealized (0 1) (0 3) (7 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xr expt)
    (xi xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 78)
  (parent 73)
  (unrealized (0 3))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 6 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b-0 (privk b-0)) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca)))))
  (label 79)
  (parent 74)
  (unrealized (0 1) (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xr expt)
    (xi xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 80)
  (parent 75)
  (unrealized (0 3))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca-0) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b-0 (privk b-0)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca-0))
          (enc n
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca-0)))))
  (label 81)
  (parent 76)
  (unrealized (0 1) (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 6 2 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 82)
  (parent 78)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 6 3 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 83)
  (parent 78)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 6 5 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 84)
  (parent 78)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr x))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) x)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 85)
  (parent 78)
  (unrealized (0 3) (6 0))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xr expt)
    (xi xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi) (xr xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 86)
  (parent 79)
  (unrealized (0 3))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 7 2 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 87)
  (parent 80)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 3 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 88)
  (parent 80)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 6 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 89)
  (parent 80)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr x))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) x)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 90)
  (parent 80)
  (unrealized (0 3) (7 0))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xr expt)
    (xi xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca-0) (xi xi) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 91)
  (parent 81)
  (unrealized (0 3))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 92)
  (parent 82)
  (unrealized (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (6 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 93)
  (parent 83)
  (unrealized (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 94)
  (parent 84)
  (unrealized (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 0 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 95)
  (parent 85)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 7 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 96)
  (parent 85)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 0) (6 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 4 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 97)
  (parent 85)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)) ((7 0) (6 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))))
  (label 98)
  (parent 85)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 7 2 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 99)
  (parent 86)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 3 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 100)
  (parent 86)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 6 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 101)
  (parent 86)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr x))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) x)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 102)
  (parent 86)
  (unrealized (0 3) (7 0))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 103)
  (parent 87)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (7 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 104)
  (parent 88)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 105)
  (parent 89)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 0 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 106)
  (parent 90)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (7 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 8 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 107)
  (parent 90)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 0) (7 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 4 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 108)
  (parent 90)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 0) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))))
  (label 109)
  (parent 90)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 8 2 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 110)
  (parent 91)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 3 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 111)
  (parent 91)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 7 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 112)
  (parent 91)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 rndx)
    (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr x))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) x)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 113)
  (parent 91)
  (unrealized (0 3) (8 0))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (6 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 114)
  (parent 92)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (7 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (6 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 115)
  (parent 93)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 1) (6 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint)
    (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 116)
  (parent 94)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 117)
  (parent 95)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (7 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 118)
  (parent 96)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (6 0)) ((4 0) (7 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 119)
  (parent 97)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 0) (6 0)) ((7 0) (8 0)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 120)
  (parent 98)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (7 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 121)
  (parent 99)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (7 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 122)
  (parent 100)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 123)
  (parent 101)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 0 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 124)
  (parent 102)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 0) (7 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 8 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 125)
  (parent 102)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (7 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 4 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 126)
  (parent 102)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 0) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))))
  (label 127)
  (parent 102)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (8 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 128)
  (parent 103)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (8 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 129)
  (parent 104)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 130)
  (parent 105)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 131)
  (parent 106)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 132)
  (parent 107)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (7 0)) ((4 0) (8 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 133)
  (parent 108)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (9 0)) ((9 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 134)
  (parent 109)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 135)
  (parent 110)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (8 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 136)
  (parent 111)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 137)
  (parent 112)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 9 0 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 138)
  (parent 113)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 0) (8 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 9 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 139)
  (parent 113)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (8 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 9 4 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 140)
  (parent 113)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)) ((8 1) (0 3)) ((9 0) (8 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))))
  (label 141)
  (parent 113)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (8 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (6 0)) ((8 1) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 142)
  (parent 114)
  (unrealized (0 3) (8 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi-0)) xi))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (8 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (6 0)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi-0)) xi))
    (hash "share" (exp (gen) (mul xi xi-0)) xi) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xi-0)) xi))))
  (label 143)
  (parent 115)
  (unrealized (0 3) (8 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 1) (6 0)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))))
  (label 144)
  (parent 116)
  (unrealized (0 3) (8 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 145)
  (parent 117)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 146)
  (parent 118)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (6 0)) ((4 0) (8 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 147)
  (parent 119)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 0) (6 0)) ((7 0) (9 0)) ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 148)
  (parent 120)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 149)
  (parent 121)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (8 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 150)
  (parent 122)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 151)
  (parent 123)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0))
    ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 152)
  (parent 124)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (7 0)) ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 153)
  (parent 125)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (7 0)) ((4 0) (8 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 154)
  (parent 126)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (9 0))
    ((9 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 155)
  (parent 127)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (9 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 156)
  (parent 128)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi-0)) xi))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (9 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi-0)) xi))
    (hash "share" (exp (gen) (mul xi xi-0)) xi) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xi-0)) xi))))
  (label 157)
  (parent 129)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))))
  (label 158)
  (parent 130)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 159)
  (parent 131)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 160)
  (parent 132)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (7 0)) ((4 0) (9 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 161)
  (parent 133)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (10 0)) ((9 1) (0 3))
    ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint)
    (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 162)
  (parent 134)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 163)
  (parent 135)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (9 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 164)
  (parent 136)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 165)
  (parent 137)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((0 0) (9 0)) ((1 0) (2 0))
    ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 166)
  (parent 138)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 167)
  (parent 139)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (8 0)) ((4 0) (9 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 168)
  (parent 140)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 0) (8 0))
    ((9 0) (10 0)) ((10 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (enc n hint
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 169)
  (parent 141)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 170)
  (parent 145)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (5 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0))
    ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 171)
  (parent 146)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr-0)) xi))
  (precedes ((0 0) (5 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (6 0)) ((4 0) (9 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr-0)) xi))
    (hash "share" (exp (gen) (mul xi xr-0)) xi) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xr-0)) xi))))
  (label 172)
  (parent 147)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
  (precedes ((0 0) (5 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 0) (6 0)) ((7 0) (10 0)) ((8 1) (0 3)) ((9 1) (8 0))
    ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))))
  (label 173)
  (parent 148)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0))
    ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 174)
  (parent 149)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi-0)) xi))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (9 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi-0)) xi))
    (hash "share" (exp (gen) (mul xi xi-0)) xi) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xi-0)) xi))))
  (label 175)
  (parent 150)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))))
  (label 176)
  (parent 151)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0))
    ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 177)
  (parent 152)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (7 0)) ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 178)
  (parent 153)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (7 0)) ((4 0) (9 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 179)
  (parent 154)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (10 0))
    ((9 1) (0 3)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint)
    (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 180)
  (parent 155)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)) ((9 1) (8 0))
    ((10 1) (9 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 181)
  (parent 159)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 0) (10 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 182)
  (parent 160)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr-0)) xi))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (7 0)) ((4 0) (10 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr-0)) xi))
    (hash "share" (exp (gen) (mul xi xr-0)) xi) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xr-0)) xi))))
  (label 183)
  (parent 161)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (11 0)) ((9 1) (0 3))
    ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))))
  (label 184)
  (parent 162)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (10 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 185)
  (parent 163)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi-0)) xi))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (10 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi-0)) xi))
    (hash "share" (exp (gen) (mul xi xi-0)) xi) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xi-0)) xi))))
  (label 186)
  (parent 164)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 1) (8 0))
    ((10 1) (9 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))))
  (label 187)
  (parent 165)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((0 0) (10 0)) ((1 0) (2 0))
    ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (0 3)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint)
    (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 188)
  (parent 166)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 0) (10 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 189)
  (parent 167)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (8 0)) ((4 0) (10 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 190)
  (parent 168)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 0) (8 0))
    ((9 0) (11 0)) ((10 1) (0 3)) ((11 1) (10 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint)
    (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 191)
  (parent 169)
  (unrealized (0 3) (11 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0))
    ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 192)
  (parent 177)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (7 0)) ((1 0) (10 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)) ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 193)
  (parent 178)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr-0)) xi))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (7 0)) ((4 0) (10 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)) ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr-0)) xi))
    (hash "share" (exp (gen) (mul xi xr-0)) xi) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xr-0)) xi))))
  (label 194)
  (parent 179)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (11 0))
    ((9 1) (0 3)) ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))))
  (label 195)
  (parent 180)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((0 0) (11 0)) ((1 0) (2 0))
    ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (0 3)) ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 196)
  (parent 188)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (7 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 0) (11 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)) ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 197)
  (parent 189)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr-0)) xi))
  (precedes ((0 0) (7 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (8 0)) ((4 0) (11 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)) ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr-0)) xi))
    (hash "share" (exp (gen) (mul xi xr-0)) xi) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xr-0)) xi))))
  (label 198)
  (parent 190)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
  (precedes ((0 0) (7 0)) ((0 0) (12 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 0) (8 0))
    ((9 0) (12 0)) ((10 1) (0 3)) ((11 1) (10 0)) ((12 1) (11 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) (11 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n hint
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))))
  (label 199)
  (parent 191)
  (unrealized (0 3) (12 0))
  (dead)
  (comment "empty cohort"))

(comment "Nothing left to do")

(defprotocol nhca-nohint diffie-hellman
  (defrole init
    (vars (xi rndx) (xr expt) (a b ca name) (n text) (hint mesg))
    (trace (send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    (non-orig (privk a) (privk ca))
    (uniq-gen xi))
  (defrole resp
    (vars (xr rndx) (xi expt) (a b ca name) (n text))
    (trace (send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    (non-orig (privk b) (privk ca))
    (uniq-gen xr))
  (defrole ca
    (vars (subject ca name) (x expt))
    (trace (recv (enc "reg" (exp (gen) x) subject (privk subject)))
      (send (enc (exp (gen) x) subject (privk ca))))
    (non-orig (privk subject)))
  (comment A diffie-hellman exchange which uses a certificate authority
    to certify lonh-term NH values))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (comment Full initiator POV No need to make extra assumptions)
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint))))))
  (label 200)
  (unrealized (0 1) (0 3))
  (origs)
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 201)
  (parent 200)
  (unrealized (0 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a ca name) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test (displaced 2 1 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi) hint (enc (exp (gen) xi) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 202)
  (parent 201)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr x))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((2 1) (0 3)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi x)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi x)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi x)) x)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 203)
  (parent 201)
  (unrealized (0 3) (2 0))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a ca name) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((1 1) (0 1)) ((2 1) (0 3)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
    (enc n (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi) hint (enc (exp (gen) xi) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))))
  (label 204)
  (parent 202)
  (unrealized (2 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a ca name) (xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((1 1) (0 1)) ((2 1) (0 3)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xr)
  (operation encryption-test (displaced 3 0 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (send (cat (exp (gen) xr) (enc (exp (gen) xr) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca)))))
  (label 205)
  (parent 203)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 1 (b b) (xr xr))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((2 1) (0 3)) ((3 0) (2 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr) b (privk b)) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))))
  (label 206)
  (parent 203)
  (unrealized (0 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a ca name) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (precedes ((0 0) (1 0)) ((0 0) (3 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 1) (2 0)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi) hint (enc (exp (gen) xi) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))))
  (label 207)
  (parent 204)
  (unrealized (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a ca name) (xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (3 0)) ((1 1) (0 1))
    ((2 1) (0 3)) ((3 1) (0 3)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xr)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
    (enc n (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (send (cat (exp (gen) xr) (enc (exp (gen) xr) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))))
  (label 208)
  (parent 205)
  (unrealized (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a ca a-0 b ca-0 name) (xi xr rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca-0) (xr xr) (xi xi))
  (precedes ((0 0) (1 0)) ((0 0) (3 2)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 3) (0 3)))
  (non-orig (privk a) (privk ca) (privk b) (privk ca-0))
  (uniq-gen xi xr)
  (operation encryption-test (displaced 3 4 resp 4)
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
        (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr)))) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca-0)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca-0))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))))
  (label 209)
  (parent 206)
  (unrealized (3 1) (3 2))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 1 (b b) (xr xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((4 1) (0 3)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
    (enc n (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))))
  (label 210)
  (parent 206)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a ca name) (xi rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi)) xi))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 1) (2 0)) ((4 1) (3 0)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xi)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi)) xi))
    (hash "share" (exp (gen) (mul xi xi)) xi) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi) hint (enc (exp (gen) xi) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint))
      (send (cat "key" (hash "share" (exp (gen) (mul xi xi)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi)) xi))
      (send (cat "share" (exp (gen) (mul xi xi)) xi))))
  (label 211)
  (parent 207)
  (unrealized (4 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a ca name) (xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (4 0)) ((1 1) (0 1))
    ((2 1) (0 3)) ((3 1) (0 3)) ((4 1) (3 0)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xr)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (send (cat (exp (gen) xr) (enc (exp (gen) xr) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))))
  (label 212)
  (parent 208)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a ca a-0 b name) (xi xr rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca) (xr xr) (xi xi))
  (precedes ((0 0) (1 0)) ((0 0) (3 2)) ((1 1) (0 1)) ((2 1) (3 1))
    ((3 0) (2 0)) ((3 3) (0 3)))
  (non-orig (privk a) (privk ca) (privk b))
  (uniq-gen xi xr)
  (operation encryption-test (displaced 4 2 ca 2)
    (enc (exp (gen) xr) b (privk ca-0)) (3 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))))
  (label 213)
  (parent 209)
  (unrealized (3 2))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a ca a-0 b ca-0 name) (xi xr rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca-0) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (3 2)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 3) (0 3)) ((4 1) (3 1)))
  (non-orig (privk a) (privk ca) (privk b) (privk ca-0))
  (uniq-gen xi xr)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr) b (privk ca-0)) (3 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca-0)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca-0))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0)))))
  (label 214)
  (parent 209)
  (unrealized (3 2))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 1 (b b) (xr xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (5 0)) ((4 1) (0 3)) ((5 1) (4 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))))
  (label 215)
  (parent 210)
  (unrealized (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a ca name) (xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
  (deflistener (cat "share" (exp (gen) (mul xr xr)) xr))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (5 0)) ((1 1) (0 1))
    ((2 1) (0 3)) ((3 1) (0 3)) ((4 1) (3 0)) ((5 1) (4 0)))
  (non-orig (privk a) (privk ca))
  (uniq-gen xr)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr xr)) xr))
    (hash "share" (exp (gen) (mul xr xr)) xr) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (send (cat (exp (gen) xr) (enc (exp (gen) xr) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint))
      (send (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr) hint)))
    ((recv (cat "share" (exp (gen) (mul xr xr)) xr))
      (send (cat "share" (exp (gen) (mul xr xr)) xr))))
  (label 216)
  (parent 212)
  (unrealized (5 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (n text) (a ca b name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((1 1) (3 2)) ((2 1) (3 1))
    ((3 0) (2 0)) ((3 3) (0 3)))
  (non-orig (privk a) (privk ca) (privk b))
  (uniq-gen xr xi)
  (operation encryption-test (displaced 4 1 ca 2)
    (enc (exp (gen) xi) a-0 (privk ca)) (3 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))))
  (label 217)
  (parent 213)
  (unrealized)
  (shape)
  (maps
    ((0)
      ((xi xi) (xr xr) (a a) (b b) (ca ca) (n n)
        (hint
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
  (origs))

(defskeleton nhca-nohint
  (vars (n text) (a ca a-0 b name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a-0) (ca ca) (x xi))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (3 1))
    ((3 0) (2 0)) ((3 3) (0 3)) ((4 1) (3 2)))
  (non-orig (privk a) (privk ca) (privk a-0) (privk b))
  (uniq-gen xr xi)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a-0 (privk ca)) (3 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a-0 (privk a-0)))
      (send (enc (exp (gen) xi) a-0 (privk ca)))))
  (label 218)
  (parent 213)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a ca b name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((1 1) (3 2)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 3) (0 3)) ((4 1) (3 1)))
  (non-orig (privk a) (privk ca) (privk b))
  (uniq-gen xr xi)
  (operation encryption-test (displaced 5 1 ca 2)
    (enc (exp (gen) xi) a-0 (privk ca-0)) (3 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 219)
  (parent 214)
  (seen 217)
  (unrealized)
  (comment "1 in cohort - 0 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a ca a-0 b ca-0 name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a-0) (b b) (ca ca-0) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a-0) (ca ca-0) (x xi))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 3) (0 3)) ((4 1) (3 1))
    ((5 1) (3 2)))
  (non-orig (privk a) (privk ca) (privk a-0) (privk b) (privk ca-0))
  (uniq-gen xr xi)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a-0 (privk ca-0)) (3 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca-0)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a-0 (privk ca-0))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a-0 (privk a-0)))
      (send (enc (exp (gen) xi) a-0 (privk ca-0)))))
  (label 220)
  (parent 214)
  (unrealized (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 1 (b b) (xr xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr)) xi))
  (precedes ((0 0) (1 0)) ((0 0) (6 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (6 0)) ((4 1) (0 3)) ((5 1) (4 0))
    ((6 1) (5 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr)) xi))
    (hash "share" (exp (gen) (mul xi xr)) xi) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b))))
    ((recv (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
      (send (cat "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr)) xi))
      (send (cat "share" (exp (gen) (mul xi xr)) xi))))
  (label 221)
  (parent 215)
  (unrealized (6 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (n text) (a ca b name) (xr xr-0 rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b b) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (3 1))
    ((3 0) (2 0)) ((3 3) (0 3)) ((4 1) (3 2)))
  (non-orig (privk a) (privk ca) (privk b))
  (uniq-gen xr xr-0)
  (operation encryption-test (displaced 5 0 resp 1)
    (enc "reg" (exp (gen) xr-0) a-0 (privk a-0)) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 222)
  (parent 218)
  (unrealized)
  (shape)
  (maps
    ((0)
      ((xi xr-0) (xr xr) (a a) (b b) (ca ca) (n n)
        (hint
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
  (origs))

(defskeleton nhca-nohint
  (vars (n text) (a ca b ca-0 name) (xr xr-0 rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b b) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand resp 4 (n n) (a a) (b b) (ca ca-0) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((1 1) (0 1)) ((2 1) (0 3))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 3) (0 3)) ((4 1) (3 1))
    ((5 1) (3 2)))
  (non-orig (privk a) (privk ca) (privk b) (privk ca-0))
  (uniq-gen xr xr-0)
  (operation encryption-test (displaced 6 0 resp 1)
    (enc "reg" (exp (gen) xr-0) a-0 (privk a-0)) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca-0)))
      (recv
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0)))))
  (label 223)
  (parent 220)
  (unrealized)
  (shape)
  (maps
    ((0)
      ((xi xr-0) (xr xr) (a a) (b b) (ca ca) (n n)
        (hint
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
  (origs))

(comment "Nothing left to do")

(defprotocol nhca-nohint diffie-hellman
  (defrole init
    (vars (xi rndx) (xr expt) (a b ca name) (n text) (hint mesg))
    (trace (send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    (non-orig (privk a) (privk ca))
    (uniq-gen xi))
  (defrole resp
    (vars (xr rndx) (xi expt) (a b ca name) (n text))
    (trace (send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    (non-orig (privk b) (privk ca))
    (uniq-gen xr))
  (defrole ca
    (vars (subject ca name) (x expt))
    (trace (recv (enc "reg" (exp (gen) x) subject (privk subject)))
      (send (enc (exp (gen) x) subject (privk ca))))
    (non-orig (privk subject)))
  (comment A diffie-hellman exchange which uses a certificate authority
    to certify lonh-term NH values))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xr rndx) (xi expt))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (comment Full responder point of view with freshly chosen n)
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr)))))))
  (label 224)
  (unrealized (0 1) (0 2) (0 4))
  (origs (n (0 3)))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xi expt) (xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr) b (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 225)
  (parent 224)
  (unrealized (0 2) (0 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test (displaced 2 1 ca 2)
    (enc (exp (gen) x) a (privk ca)) (0 2))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 226)
  (parent 225)
  (unrealized (0 4))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xr rndx) (x expt))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi x))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x x))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((2 1) (0 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) a (privk ca)) (0 2))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) x) (enc (exp (gen) x) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr x)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr x)) x)
              (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr x)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr x)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) x) a (privk a)))
      (send (enc (exp (gen) x) a (privk ca)))))
  (label 227)
  (parent 225)
  (unrealized (0 4) (2 0))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((1 1) (0 1)) ((2 1) (0 4)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))) (0 4))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
  (label 228)
  (parent 226)
  (unrealized (2 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((1 1) (0 1)) ((2 1) (0 2)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test (displaced 3 0 resp 1)
    (enc "reg" (exp (gen) xr-0) a (privk a)) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 229)
  (parent 227)
  (unrealized (0 4))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xr xr-0 rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand resp 1 (b a) (xr xr-0))
  (precedes ((0 0) (1 0)) ((1 1) (0 1)) ((2 1) (0 2)) ((3 0) (2 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) a (privk a)) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))))
  (label 230)
  (parent 227)
  (unrealized (0 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (3 0)) ((1 1) (0 1)) ((2 1) (0 4))
    ((3 1) (2 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))) (2 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
  (label 231)
  (parent 228)
  (unrealized (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (3 0)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 1) (0 4)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))) (0 4))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
  (label 232)
  (parent 229)
  (unrealized (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca a b-0 ca-0 name) (xr xi rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b-0) (ca ca-0) (xi xi) (xr xr))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 4) (0 4)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (displaced 3 4 init 5)
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr)))) (0 4))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b-0 (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))))
  (label 233)
  (parent 230)
  (unrealized (3 1) (3 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xr xr-0 rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand resp 1 (b a) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (4 0)) ((4 1) (0 4)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
    (0 4))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
  (label 234)
  (parent 230)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener (cat "share" (exp (gen) (mul xr xr)) xr))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((1 1) (0 1)) ((2 1) (0 4))
    ((3 1) (2 0)) ((4 1) (3 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr xr)) xr))
    (hash "share" (exp (gen) (mul xr xr)) xr) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv (cat "share" (exp (gen) (mul xr xr)) xr))
      (send (cat "share" (exp (gen) (mul xr xr)) xr))))
  (label 235)
  (parent 231)
  (unrealized (4 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (4 0)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 1) (0 4)) ((4 1) (3 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
  (label 236)
  (parent 232)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca a b-0 name) (xr xi rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b-0) (ca ca) (xi xi) (xr xr))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((2 1) (3 1)) ((3 0) (2 0)) ((3 4) (0 4)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (displaced 4 2 ca 2)
    (enc (exp (gen) xi) a (privk ca-0)) (3 1))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b-0 (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))))
  (label 237)
  (parent 233)
  (unrealized (3 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca a b-0 ca-0 name) (xr xi rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b-0) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 4) (0 4)) ((4 1) (3 1)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a (privk ca-0)) (3 1))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b-0 (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0)))))
  (label 238)
  (parent 233)
  (unrealized (3 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xr xr-0 rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand resp 1 (b a) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (5 0)) ((4 1) (0 4)) ((5 1) (4 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
        (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
    (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
  (label 239)
  (parent 234)
  (unrealized (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca name) (xr rndx))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr) (xi xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
  (deflistener (cat "share" (exp (gen) (mul xr xr)) xr))
  (precedes ((0 0) (1 0)) ((0 0) (2 0)) ((0 0) (5 0)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 1) (0 4)) ((4 1) (3 0)) ((5 1) (4 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr xr)) xr))
    (hash "share" (exp (gen) (mul xr xr)) xr) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr) (enc (exp (gen) xr) b (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr)) xr)))))
    ((recv (cat "share" (exp (gen) (mul xr xr)) xr))
      (send (cat "share" (exp (gen) (mul xr xr)) xr))))
  (label 240)
  (parent 236)
  (unrealized (5 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (n text) (b ca a name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((2 1) (3 1)) ((3 0) (2 0)) ((3 4) (0 4)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 4 1 ca 2)
    (enc (exp (gen) xr) b-0 (privk ca)) (3 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))))
  (label 241)
  (parent 237)
  (unrealized)
  (shape)
  (maps ((0) ((n n) (xr xr) (xi xi) (a a) (b b) (ca ca))))
  (origs (n (0 3))))

(defskeleton nhca-nohint
  (vars (n text) (b ca a b-0 name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b-0) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b-0) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((0 3) (3 3)) ((1 1) (0 1))
    ((2 1) (0 2)) ((2 1) (3 1)) ((3 0) (2 0)) ((3 4) (0 4))
    ((4 1) (3 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk b-0))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr) b-0 (privk ca)) (3 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b-0 (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b-0 (privk b-0)))
      (send (enc (exp (gen) xr) b-0 (privk ca)))))
  (label 242)
  (parent 237)
  (unrealized (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca a name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (1 0)) ((0 3) (3 3)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (4 0)) ((3 4) (0 4)) ((4 1) (3 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 5 1 ca 2)
    (enc (exp (gen) xr) b-0 (privk ca-0)) (3 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 243)
  (parent 238)
  (unrealized)
  (shape)
  (maps ((0) ((n n) (xr xr) (xi xi) (a a) (b b) (ca ca))))
  (origs (n (0 3))))

(defskeleton nhca-nohint
  (vars (n text) (b ca a b-0 ca-0 name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b-0) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b-0) (ca ca-0) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((0 3) (3 3)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 0) (2 0)) ((3 0) (4 0)) ((3 4) (0 4))
    ((4 1) (3 1)) ((5 1) (3 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk b-0) (privk ca-0))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr) b-0 (privk ca-0)) (3 3))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b-0 (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b-0 (privk b-0)))
      (send (enc (exp (gen) xr) b-0 (privk ca-0)))))
  (label 244)
  (parent 238)
  (unrealized (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xr xr-0 rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand resp 1 (b a) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
      (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
  (deflistener (cat "share" (exp (gen) (mul xr xr-0)) xr))
  (precedes ((0 0) (1 0)) ((0 0) (6 0)) ((1 1) (0 1)) ((2 1) (0 2))
    ((3 0) (2 0)) ((3 0) (6 0)) ((4 1) (0 4)) ((5 1) (4 0))
    ((6 1) (5 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr xr-0)) xr))
    (hash "share" (exp (gen) (mul xr xr-0)) xr) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
         (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))))
    ((recv (cat "share" (exp (gen) (mul xr xr-0)) xr))
      (send (cat "share" (exp (gen) (mul xr xr-0)) xr))))
  (label 245)
  (parent 239)
  (unrealized (6 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (n text) (b ca a name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (4 0)) ((0 3) (3 3)) ((1 1) (0 1))
    ((2 1) (0 2)) ((2 1) (3 1)) ((3 0) (2 0)) ((3 4) (0 4))
    ((4 1) (3 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 5 0 resp 1)
    (enc "reg" (exp (gen) xr) b-0 (privk b-0)) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 246)
  (parent 242)
  (seen 241)
  (unrealized)
  (comment "1 in cohort - 0 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (b ca a ca-0 name) (xi xr rndx))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (precedes ((0 0) (1 0)) ((0 0) (5 0)) ((0 3) (3 3)) ((1 1) (0 1))
    ((2 1) (0 2)) ((3 0) (2 0)) ((3 0) (4 0)) ((3 4) (0 4))
    ((4 1) (3 1)) ((5 1) (3 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 6 0 resp 1)
    (enc "reg" (exp (gen) xr) b-0 (privk b-0)) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0)))))
  (label 247)
  (parent 244)
  (unrealized)
  (shape)
  (maps ((0) ((n n) (xr xr) (xi xi) (a a) (b b) (ca ca))))
  (origs (n (0 3))))

(comment "Nothing left to do")

(defprotocol nhca-nohint diffie-hellman
  (defrole init
    (vars (xi rndx) (xr expt) (a b ca name) (n text) (hint mesg))
    (trace (send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    (non-orig (privk a) (privk ca))
    (uniq-gen xi))
  (defrole resp
    (vars (xr rndx) (xi expt) (a b ca name) (n text))
    (trace (send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    (non-orig (privk b) (privk ca))
    (uniq-gen xr))
  (defrole ca
    (vars (subject ca name) (x expt))
    (trace (recv (enc "reg" (exp (gen) x) subject (privk subject)))
      (send (enc (exp (gen) x) subject (privk ca))))
    (non-orig (privk subject)))
  (comment A diffie-hellman exchange which uses a certificate authority
    to certify lonh-term NH values))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx)
    (xr-0 xi-0 expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi-0))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (uniq-orig n)
  (comment point of view in which init and resp each complete and they
    agree on the relevant parameters)
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
  (label 248)
  (unrealized (0 1) (0 3) (1 1) (1 2) (1 4))
  (preskeleton)
  (origs (n (1 3)))
  (comment "Not a skeleton"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi xr rndx)
    (xr-0 xi-0 expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi-0))
  (precedes ((1 3) (0 3)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (uniq-orig n)
  (comment point of view in which init and resp each complete and they
    agree on the relevant parameters)
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
  (label 249)
  (parent 248)
  (unrealized (0 1) (0 3) (1 1) (1 2) (1 4))
  (origs (n (1 3)))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr xi-0 expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr-0) b (privk ca)) (1 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca)))))
  (label 250)
  (parent 249)
  (unrealized (0 1) (0 3) (1 2) (1 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 3 2 ca 2)
    (enc (exp (gen) x) a (privk ca)) (1 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca)))))
  (label 251)
  (parent 250)
  (unrealized (0 1) (0 3) (1 4))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi x))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x x))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) a (privk ca)) (1 2))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) x) (enc (exp (gen) x) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 x)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 x)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 x)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 x)) x)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 x)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 x)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 x)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) x) a (privk a)))
      (send (enc (exp (gen) x) a (privk ca)))))
  (label 252)
  (parent 250)
  (unrealized (0 1) (0 3) (1 4) (3 0))
  (comment "3 in cohort - 3 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 4)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
  (label 253)
  (parent 251)
  (unrealized (0 1) (0 3) (3 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xr-1)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (precedes ((0 0) (3 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test (displaced 4 0 resp 1)
    (enc "reg" (exp (gen) xr-2) a (privk a)) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))
      (recv (enc (exp (gen) xr-1) a (privk ca)))
      (send (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca)))))
  (label 254)
  (parent 252)
  (unrealized (0 1) (0 3) (1 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 4 1 resp 1)
    (enc "reg" (exp (gen) xr-1) a (privk a)) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca)))))
  (label 255)
  (parent 252)
  (unrealized (0 1) (0 3) (1 4))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (defstrand resp 1 (b a) (xr xr-1))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-1) a (privk a)) (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))))
  (label 256)
  (parent 252)
  (unrealized (0 1) (0 3) (1 4))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (4 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 4)) ((4 1) (3 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))
    (3 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
  (label 257)
  (parent 253)
  (unrealized (0 1) (0 3) (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xi xr rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (3 0)) ((0 4) (1 4)) ((1 0) (2 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (1 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr)
  (uniq-orig n)
  (operation encryption-test (displaced 4 0 init 5)
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xi)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 258)
  (parent 254)
  (unrealized (0 1))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xr-1)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (precedes ((0 0) (3 0)) ((0 0) (4 0)) ((1 0) (2 0)) ((1 0) (4 0))
    ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))
      (recv (enc (exp (gen) xr-1) a (privk ca)))
      (send (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
  (label 259)
  (parent 254)
  (unrealized (0 1) (0 3) (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 0) (4 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
  (label 260)
  (parent 255)
  (unrealized (0 1) (0 3) (4 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a b-0 ca-0 name) (xi rndx) (xr expt)
    (xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca-0) (xi xi-0) (xr xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 4) (1 4)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 4 5 init 5)
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))))
  (label 261)
  (parent 256)
  (unrealized (0 1) (0 3) (4 1) (4 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (defstrand resp 1 (b a) (xr xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((5 1) (1 4)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (enc "check" n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (1 4))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-1) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
  (label 262)
  (parent 256)
  (unrealized (0 1) (0 3) (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 4)) ((4 1) (3 0)) ((5 1) (4 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 263)
  (parent 257)
  (unrealized (0 1) (0 3) (5 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (3 0)) ((0 4) (1 4)) ((1 0) (2 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (0 1)) ((3 1) (1 2)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (displaced 4 3 ca 2)
    (enc (exp (gen) xi) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 264)
  (parent 258)
  (unrealized)
  (shape)
  (maps
    ((0 1)
      ((a a) (b b) (ca ca) (xi xi) (xr xr) (n n) (xr-0 xr)
        (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr)))
        (xi-0 xi))))
  (origs (n (1 3))))

(defskeleton nhca-nohint
  (vars (n text) (a b ca name) (xr xi rndx))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (3 0)) ((0 0) (4 0)) ((0 4) (1 4)) ((1 0) (2 0))
    ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (0 1)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr xi)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr)))))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 265)
  (parent 258)
  (unrealized)
  (shape)
  (maps
    ((0 1)
      ((a a) (b b) (ca ca) (xi xi) (xr xr) (n n) (xr-0 xr)
        (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi)) xr)))
        (xi-0 xi))))
  (origs (n (1 3))))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xr-1)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (precedes ((0 0) (3 0)) ((0 0) (5 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4))
    ((5 1) (4 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))
    (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))
      (recv (enc (exp (gen) xr-1) a (privk ca)))
      (send (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
  (label 266)
  (parent 259)
  (unrealized (0 1) (0 3) (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4)) ((5 1) (4 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))
    (4 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
  (label 267)
  (parent 260)
  (unrealized (0 1) (0 3) (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a b-0 name) (xi rndx) (xr expt)
    (xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca) (xi xi-0) (xr xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 5 3 ca 2)
    (enc (exp (gen) xi-0) a (privk ca-0)) (4 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))))
  (label 268)
  (parent 261)
  (unrealized (0 1) (0 3) (4 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a b-0 ca-0 name) (xi rndx) (xr expt)
    (xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca-0) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca-0)) (4 1))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xi-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0)))))
  (label 269)
  (parent 261)
  (unrealized (0 1) (0 3) (4 3))
  (comment "2 in cohort - 2 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (defstrand resp 1 (b a) (xr xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (precedes ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (6 0)) ((5 1) (1 4))
    ((6 1) (5 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
        (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))
    (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-1) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
  (label 270)
  (parent 262)
  (unrealized (0 1) (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xr expt) (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xr-1)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
  (precedes ((0 0) (3 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4))
    ((5 1) (4 0)) ((6 1) (5 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-1) a (privk a)))
      (recv (enc (exp (gen) xr-1) a (privk ca)))
      (send (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr-1)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-1)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (label 271)
  (parent 266)
  (unrealized (0 1) (0 3) (6 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca name) (xi rndx) (xr expt)
    (xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a b) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a b) (b b) (ca ca) (xr xr-0) (xi xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (3 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 1) (1 4)) ((5 1) (4 0))
    ((6 1) (5 0)))
  (non-orig (privk b) (privk ca))
  (uniq-gen xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) b (privk b)))
      (recv (enc (exp (gen) xi) b (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) b (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) b (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)))))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 272)
  (parent 267)
  (unrealized (0 1) (0 3) (6 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi-0) (xr xr-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 5 2 ca 2)
    (enc (exp (gen) xr-0) b-0 (privk ca)) (4 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))))
  (label 273)
  (parent 268)
  (unrealized (0 1) (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a b-0 name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject b-0) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk b-0))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr-0) b-0 (privk ca)) (4 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xr-0) b-0 (privk b-0)))
      (send (enc (exp (gen) xr-0) b-0 (privk ca)))))
  (label 274)
  (parent 268)
  (unrealized (0 1) (0 3) (5 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 6 2 ca 2)
    (enc (exp (gen) xr-0) b-0 (privk ca-0)) (4 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 275)
  (parent 269)
  (unrealized (0 1) (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a b-0 ca-0 name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b-0) (ca ca-0) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject b-0) (ca ca-0) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk b-0) (privk ca-0))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xr-0) b-0 (privk ca-0)) (4 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b-0 (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) b-0 (privk b-0)))
      (send (enc (exp (gen) xr-0) b-0 (privk ca-0)))))
  (label 276)
  (parent 269)
  (unrealized (0 1) (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (a b ca name) (xi rndx) (xr expt)
    (xr-0 xr-1 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xr-1))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-1))
  (defstrand resp 1 (b a) (xr xr-1))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
      (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (7 0)) ((1 3) (0 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (7 0)) ((5 1) (1 4))
    ((6 1) (5 0)) ((7 1) (6 0)))
  (non-orig (privk a) (privk b) (privk ca))
  (uniq-gen xi xr-0 xr-1)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xr-1) (enc (exp (gen) xr-1) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-1)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-1) a (privk a)))
      (send (enc (exp (gen) xr-1) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-1) a (privk a))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
         (hash "hint" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)
          (hash "hint"
            (hash "share" (exp (gen) (mul xr-0 xr-1)) xr-0)))))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-1)) xr-0))))
  (label 277)
  (parent 270)
  (unrealized (0 1) (0 3) (7 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xr expt)
    (xi xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 278)
  (parent 273)
  (unrealized (0 3))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 6 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b-0 (privk b-0)) (5 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca)))))
  (label 279)
  (parent 274)
  (unrealized (0 1) (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xr expt)
    (xi xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 280)
  (parent 275)
  (unrealized (0 3))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi rndx) (xr expt)
    (xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca-0) (xi xi-0) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr-0))
  (precedes ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b-0 (privk b-0)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi) hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca-0)))))
  (label 281)
  (parent 276)
  (unrealized (0 1) (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 6 2 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 282)
  (parent 278)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 6 3 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 283)
  (parent 278)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 6 5 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 284)
  (parent 278)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr x))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) x)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 285)
  (parent 278)
  (unrealized (0 3) (6 0))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xr expt)
    (xi xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca) (xi xi) (xr xr-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 286)
  (parent 279)
  (unrealized (0 3))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 7 2 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 287)
  (parent 280)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 3 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 288)
  (parent 280)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 6 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 289)
  (parent 280)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr x))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) x)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 290)
  (parent 280)
  (unrealized (0 3) (7 0))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xr expt)
    (xi xr-0 xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr-0) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))
    (n n) (a a) (b b) (ca ca-0) (xi xi) (xr xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr-0 xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) xi-0) a (privk ca)) (0 1))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))
      (recv (enc (exp (gen) xr-0) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
            (hash "hint"
              (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr-0)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr-0)) xr-0))
          (enc (exp (gen) xr-0) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr-0)) xr-0)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 291)
  (parent 281)
  (unrealized (0 3))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 292)
  (parent 282)
  (unrealized (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (6 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 293)
  (parent 283)
  (unrealized (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 294)
  (parent 284)
  (unrealized (0 3) (6 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 0 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 295)
  (parent 285)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 7 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 296)
  (parent 285)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 0) (6 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 4 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 297)
  (parent 285)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (precedes ((0 0) (5 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3)) ((7 0) (6 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))))
  (label 298)
  (parent 285)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 7 2 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 299)
  (parent 286)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 3 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 300)
  (parent 286)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 7 6 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 301)
  (parent 286)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 rndx) (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr x))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) x)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 302)
  (parent 286)
  (unrealized (0 3) (7 0))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 303)
  (parent 287)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (7 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 304)
  (parent 288)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 305)
  (parent 289)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 0 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 306)
  (parent 290)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (7 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 8 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 307)
  (parent 290)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 0) (7 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 4 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 308)
  (parent 290)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 0) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))))
  (label 309)
  (parent 290)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 8 2 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 310)
  (parent 291)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 3 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca)))))
  (label 311)
  (parent 291)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 7 ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca)))))
  (label 312)
  (parent 291)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 rndx)
    (x expt))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr x))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x x))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test (added-strand ca 2)
    (enc (exp (gen) x) b (privk ca)) (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) x) hint (enc (exp (gen) x) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 x)) x)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) x) b (privk b)))
      (send (enc (exp (gen) x) b (privk ca)))))
  (label 313)
  (parent 291)
  (unrealized (0 3) (8 0))
  (comment "4 in cohort - 4 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (6 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 314)
  (parent 292)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (7 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (6 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint) (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 315)
  (parent 293)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 1) (6 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint)
    (6 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 316)
  (parent 294)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 317)
  (parent 295)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (7 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 318)
  (parent 296)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (5 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (6 0)) ((4 0) (7 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 319)
  (parent 297)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 0) (6 0)) ((7 0) (8 0)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 320)
  (parent 298)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (7 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 321)
  (parent 299)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (7 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 322)
  (parent 300)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 323)
  (parent 301)
  (unrealized (0 3) (7 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 0 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 324)
  (parent 302)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 0) (7 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 8 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 325)
  (parent 302)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (7 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 8 4 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 326)
  (parent 302)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (precedes ((0 0) (6 0)) ((1 0) (2 0)) ((1 0) (5 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 0) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))))
  (label 327)
  (parent 302)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (8 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 328)
  (parent 303)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (8 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 329)
  (parent 304)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 330)
  (parent 305)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 331)
  (parent 306)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 332)
  (parent 307)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (7 0)) ((4 0) (8 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 333)
  (parent 308)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (9 0)) ((9 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 334)
  (parent 309)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 335)
  (parent 310)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (8 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 336)
  (parent 311)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 337)
  (parent 312)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 9 0 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 338)
  (parent 313)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 0) (8 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test (displaced 9 1 resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca)))))
  (label 339)
  (parent 313)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (8 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test (displaced 9 4 resp 1)
    (enc "reg" (exp (gen) xr-1) b (privk b)) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca)))))
  (label 340)
  (parent 313)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (precedes ((0 0) (7 0)) ((1 0) (2 0)) ((1 0) (6 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3))
    ((7 1) (0 1)) ((8 1) (0 3)) ((9 0) (8 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test (added-strand resp 1)
    (enc "reg" (exp (gen) xr-0) b (privk b)) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b)))))
  (label 341)
  (parent 313)
  (unrealized (0 3))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (8 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (6 0)) ((8 1) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 342)
  (parent 314)
  (unrealized (0 3) (8 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi-0)) xi))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (8 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (6 0)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi-0)) xi))
    (hash "share" (exp (gen) (mul xi xi-0)) xi) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xi-0)) xi))))
  (label 343)
  (parent 315)
  (unrealized (0 3) (8 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 1) (6 0)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))))
  (label 344)
  (parent 316)
  (unrealized (0 3) (8 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 345)
  (parent 317)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 346)
  (parent 318)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (5 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (6 0)) ((4 0) (8 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 347)
  (parent 319)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (5 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 0) (6 0)) ((7 0) (9 0)) ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 348)
  (parent 320)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 349)
  (parent 321)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (8 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint) (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 350)
  (parent 322)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint)
    (7 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 351)
  (parent 323)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (8 0)) ((1 0) (2 0))
    ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 352)
  (parent 324)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (7 0)) ((1 0) (8 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 353)
  (parent 325)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (8 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (7 0)) ((4 0) (8 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 354)
  (parent 326)
  (unrealized (0 3) (8 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (9 0))
    ((9 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 355)
  (parent 327)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (9 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 356)
  (parent 328)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi-0)) xi))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (9 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi-0)) xi))
    (hash "share" (exp (gen) (mul xi xi-0)) xi) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xi-0)) xi))))
  (label 357)
  (parent 329)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))))
  (label 358)
  (parent 330)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 359)
  (parent 331)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 360)
  (parent 332)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (7 0)) ((4 0) (9 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 361)
  (parent 333)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (10 0)) ((9 1) (0 3))
    ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint)
    (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 362)
  (parent 334)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 363)
  (parent 335)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (9 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))))
  (label 364)
  (parent 336)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint))))
  (label 365)
  (parent 337)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((0 0) (9 0)) ((1 0) (2 0))
    ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 366)
  (parent 338)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 367)
  (parent 339)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (8 0)) ((4 0) (9 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 368)
  (parent 340)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 0) (8 0))
    ((9 0) (10 0)) ((10 1) (0 3)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (enc n
      (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (0 3))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 369)
  (parent 341)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((0 0) (5 0)) ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1))
    ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 370)
  (parent 345)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (5 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0))
    ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 371)
  (parent 346)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr-0)) xi))
  (precedes ((0 0) (5 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 0) (6 0)) ((4 0) (9 0)) ((4 4) (1 4))
    ((5 1) (0 1)) ((6 1) (0 3)) ((7 1) (0 3)) ((8 1) (7 0))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr-0)) xi))
    (hash "share" (exp (gen) (mul xi xr-0)) xi) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xr-0)) xi))))
  (label 372)
  (parent 347)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
  (precedes ((0 0) (5 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1))
    ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (0 1)) ((6 1) (0 3))
    ((7 0) (6 0)) ((7 0) (10 0)) ((8 1) (0 3)) ((9 1) (8 0))
    ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))))
  (label 373)
  (parent 348)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0))
    ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 374)
  (parent 349)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi-0)) xi))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (9 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi-0)) xi))
    (hash "share" (exp (gen) (mul xi xi-0)) xi) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xi-0)) xi))))
  (label 375)
  (parent 350)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (7 0)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))))
  (label 376)
  (parent 351)
  (unrealized (0 3) (9 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (9 0)) ((1 0) (2 0))
    ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 377)
  (parent 352)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (7 0)) ((1 0) (9 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 378)
  (parent 353)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (6 0)) ((0 0) (9 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (7 0)) ((4 0) (9 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)) ((9 1) (8 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint) (8 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 379)
  (parent 354)
  (unrealized (0 3) (9 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (10 0))
    ((9 1) (0 3)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint)
    (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 380)
  (parent 355)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3)) ((9 1) (8 0))
    ((10 1) (9 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 381)
  (parent 359)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (7 0))
    ((1 0) (10 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 382)
  (parent 360)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr-0)) xi))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 0) (7 0)) ((4 0) (10 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr-0)) xi))
    (hash "share" (exp (gen) (mul xi xr-0)) xi) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xr-0)) xi))))
  (label 383)
  (parent 361)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 3) (0 3))
    ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0))
    ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (0 1))
    ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (11 0)) ((9 1) (0 3))
    ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))))
  (label 384)
  (parent 362)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (10 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 385)
  (parent 363)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xi-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xi-0)) xi))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (10 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xi-0)) xi))
    (hash "share" (exp (gen) (mul xi xi-0)) xi) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xi-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xi-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xi-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xi-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xi-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xi-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xi-0)) xi))))
  (label 386)
  (parent 364)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xi-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi-0)
    (xr xi-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 1) (8 0))
    ((10 1) (9 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xi-0) hint (enc (exp (gen) xi-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xi-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xi-0)) xi-0))))
  (label 387)
  (parent 365)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((0 0) (10 0)) ((1 0) (2 0))
    ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (0 3)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint)
    (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint))))
  (label 388)
  (parent 366)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 0) (10 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)
    (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint))))
  (label 389)
  (parent 367)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (precedes ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (8 0)) ((4 0) (10 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))))
  (label 390)
  (parent 368)
  (unrealized (0 3) (10 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (precedes ((0 0) (7 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 0) (8 0))
    ((9 0) (11 0)) ((10 1) (0 3)) ((11 1) (10 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener
      (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint)
    (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint))))
  (label 391)
  (parent 369)
  (unrealized (0 3) (11 0))
  (comment "1 in cohort - 1 not yet seen"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((0 0) (6 0)) ((0 0) (7 0)) ((0 0) (10 0)) ((1 0) (2 0))
    ((1 0) (5 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4))
    ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3)) ((8 1) (0 3))
    ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 392)
  (parent 377)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 0) (7 0)) ((1 0) (10 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((3 1) (4 1)) ((4 0) (3 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)) ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 393)
  (parent 378)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr-0)) xi))
  (precedes ((0 0) (6 0)) ((0 0) (10 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 0) (7 0)) ((4 0) (10 0))
    ((4 4) (1 4)) ((5 1) (4 3)) ((6 1) (0 1)) ((7 1) (0 3))
    ((8 1) (0 3)) ((9 1) (8 0)) ((10 1) (9 0)))
  (non-orig (privk ca) (privk a))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr-0)) xi))
    (hash "share" (exp (gen) (mul xi xr-0)) xi) (9 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xr-0)) xi))))
  (label 394)
  (parent 379)
  (unrealized (0 3) (10 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca) (xi xi) (xr xr))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
  (precedes ((0 0) (6 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 0) (5 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((3 1) (4 1)) ((4 0) (3 0)) ((4 4) (1 4)) ((5 1) (4 3))
    ((6 1) (0 1)) ((7 1) (0 3)) ((8 0) (7 0)) ((8 0) (11 0))
    ((9 1) (0 3)) ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk b) (privk ca) (privk a))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))))
  (label 395)
  (parent 380)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xi xr xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xr-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b a) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
  (precedes ((0 0) (7 0)) ((0 0) (8 0)) ((0 0) (11 0)) ((1 0) (2 0))
    ((1 0) (6 0)) ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1))
    ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4))
    ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3))
    ((9 1) (0 3)) ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
    (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca)))
      (send (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xr-0 xr-0)) xr-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))
      (send (cat "share" (exp (gen) (mul xr-0 xr-0)) xr-0))))
  (label 396)
  (parent 388)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xi-0 xr rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
  (precedes ((0 0) (7 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 0) (8 0)) ((1 0) (11 0)) ((1 3) (0 3)) ((1 3) (4 3))
    ((2 1) (1 1)) ((3 1) (1 2)) ((4 0) (3 0)) ((4 0) (5 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)) ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xi-0 xr)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr) hint (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xr)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr)) xi-0) hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr)) xi-0))))
  (label 397)
  (parent 389)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (ca a ca-0 name) (xr xi xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b a) (ca ca) (xi xi)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b a) (ca ca) (xr xr) (xi xr-0))
  (defstrand ca 2 (subject a) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr)))
    (n n) (a a) (b a) (ca ca-0) (xi xr-0) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr-0))
  (defstrand ca 2 (subject a) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand ca 2 (subject a) (ca ca) (x xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
  (deflistener (cat "share" (exp (gen) (mul xi xr-0)) xi))
  (precedes ((0 0) (7 0)) ((0 0) (11 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 0) (8 0)) ((4 0) (11 0))
    ((4 4) (1 4)) ((5 1) (4 1)) ((6 1) (4 3)) ((7 1) (0 1))
    ((8 1) (0 3)) ((9 1) (0 3)) ((10 1) (9 0)) ((11 1) (10 0)))
  (non-orig (privk ca) (privk a) (privk ca-0))
  (uniq-gen xr xi xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi xr-0)) xi))
    (hash "share" (exp (gen) (mul xi xr-0)) xi) (10 0))
  (traces
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) a (privk a)))
      (recv (enc (exp (gen) xr) a (privk ca)))
      (recv (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
            (hash "hint"
              (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) a (privk a)))
      (recv (enc (exp (gen) xr-0) a (privk ca-0)))
      (send
        (cat (exp (gen) xr-0) (enc (exp (gen) xr-0) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xr xr-0)) xr))
          (enc (exp (gen) xr) a (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr-0)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xr xr-0)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xr xr-0)) xr)))))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) a (privk a)))
      (send (enc (exp (gen) xr) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) a (privk a)))
      (send (enc (exp (gen) xr-0) a (privk ca))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi xr-0)) xi) hint)))
    ((recv (cat "share" (exp (gen) (mul xi xr-0)) xi))
      (send (cat "share" (exp (gen) (mul xi xr-0)) xi))))
  (label 398)
  (parent 390)
  (unrealized (0 3) (11 0))
  (dead)
  (comment "empty cohort"))

(defskeleton nhca-nohint
  (vars (hint mesg) (n text) (b ca a ca-0 name) (xi xr xi-0 xr-0 rndx))
  (defstrand init 5 (hint hint) (n n) (a a) (b b) (ca ca) (xi xi-0)
    (xr xr-0))
  (defstrand resp 5 (n n) (a a) (b b) (ca ca) (xr xr) (xi xi))
  (defstrand ca 2 (subject b) (ca ca) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi))
  (defstrand init 5
    (hint (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))) (n n)
    (a a) (b b) (ca ca-0) (xi xi) (xr xr))
  (defstrand ca 2 (subject a) (ca ca-0) (x xi))
  (defstrand ca 2 (subject b) (ca ca-0) (x xr))
  (defstrand ca 2 (subject a) (ca ca) (x xi-0))
  (defstrand ca 2 (subject b) (ca ca) (x xr-0))
  (defstrand resp 1 (b b) (xr xr-0))
  (deflistener
    (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener
    (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
  (deflistener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
  (precedes ((0 0) (7 0)) ((0 0) (12 0)) ((1 0) (2 0)) ((1 0) (6 0))
    ((1 3) (0 3)) ((1 3) (4 3)) ((2 1) (1 1)) ((3 1) (1 2))
    ((4 0) (3 0)) ((4 0) (5 0)) ((4 4) (1 4)) ((5 1) (4 1))
    ((6 1) (4 3)) ((7 1) (0 1)) ((8 1) (0 3)) ((9 0) (8 0))
    ((9 0) (12 0)) ((10 1) (0 3)) ((11 1) (10 0)) ((12 1) (11 0)))
  (non-orig (privk b) (privk ca) (privk a) (privk ca-0))
  (uniq-gen xi xr xi-0 xr-0)
  (uniq-orig n)
  (operation encryption-test
    (added-listener (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
    (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) (11 0))
  (traces
    ((send (enc "reg" (exp (gen) xi-0) a (privk a)))
      (recv (enc (exp (gen) xi-0) a (privk ca)))
      (send (cat (exp (gen) xi-0) (enc (exp (gen) xi-0) a (privk ca))))
      (recv
        (cat (exp (gen) xr-0) hint (enc (exp (gen) xr-0) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
              hint))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xr-0)
              hint)))))
    ((send (enc "reg" (exp (gen) xr) b (privk b)))
      (recv (enc (exp (gen) xr) b (privk ca)))
      (recv (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca))))
      (send
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (recv
        (enc "check" n
          (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
            (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca))))
    ((send (enc "reg" (exp (gen) xi) a (privk a)))
      (recv (enc (exp (gen) xi) a (privk ca-0)))
      (send (cat (exp (gen) xi) (enc (exp (gen) xi) a (privk ca-0))))
      (recv
        (cat (exp (gen) xr)
          (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))
          (enc (exp (gen) xr) b (privk ca-0))
          (enc n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr))))))
      (send
        (cat
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xi)
              (hash "hint" (hash "share" (exp (gen) (mul xi xr)) xr))))
          (enc "check" n
            (hash "key" (hash "share" (exp (gen) (mul xi xr)) xr)
              (hash "hint"
                (hash "share" (exp (gen) (mul xi xr)) xr)))))))
    ((recv (enc "reg" (exp (gen) xi) a (privk a)))
      (send (enc (exp (gen) xi) a (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xr) b (privk b)))
      (send (enc (exp (gen) xr) b (privk ca-0))))
    ((recv (enc "reg" (exp (gen) xi-0) a (privk a)))
      (send (enc (exp (gen) xi-0) a (privk ca))))
    ((recv (enc "reg" (exp (gen) xr-0) b (privk b)))
      (send (enc (exp (gen) xr-0) b (privk ca))))
    ((send (enc "reg" (exp (gen) xr-0) b (privk b))))
    ((recv
       (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
         hint))
      (send
        (hash "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv
       (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0) hint))
      (send
        (cat "key" (hash "share" (exp (gen) (mul xi-0 xr-0)) xi-0)
          hint)))
    ((recv (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))
      (send (cat "share" (exp (gen) (mul xi-0 xr-0)) xi-0))))
  (label 399)
  (parent 391)
  (unrealized (0 3) (12 0))
  (dead)
  (comment "empty cohort"))

(comment "Nothing left to do")