PrimeField

Documentation

data P

A large, safe prime, p = 2q + 1, where q is a large prime

Instances

Eq P

Methods

(==) :: P -> P -> Bool

(/=) :: P -> P -> Bool

Ord P

Methods

compare :: P -> P -> Ordering

(<) :: P -> P -> Bool

(<=) :: P -> P -> Bool

(>) :: P -> P -> Bool

(>=) :: P -> P -> Bool

max :: P -> P -> P

min :: P -> P -> P

Show P

Methods

showsPrec :: Int -> P -> ShowS

show :: P -> String

showList :: [P] -> ShowS

unP :: P -> Integer

data Q

A large prime such that p = 2q + 1 and p is also prime

Instances

Eq Q

Methods

(==) :: Q -> Q -> Bool

(/=) :: Q -> Q -> Bool

Ord Q

Methods

compare :: Q -> Q -> Ordering

(<) :: Q -> Q -> Bool

(<=) :: Q -> Q -> Bool

(>) :: Q -> Q -> Bool

(>=) :: Q -> Q -> Bool

max :: Q -> Q -> Q

min :: Q -> Q -> Q

Show Q

Methods

showsPrec :: Int -> Q -> ShowS

show :: Q -> String

showList :: [Q] -> ShowS

unQ :: Q -> Integer

data G

A generator order Q for prime field order P

Instances

Eq G

Methods

(==) :: G -> G -> Bool

(/=) :: G -> G -> Bool

Ord G

Methods

compare :: G -> G -> Ordering

(<) :: G -> G -> Bool

(<=) :: G -> G -> Bool

(>) :: G -> G -> Bool

(>=) :: G -> G -> Bool

max :: G -> G -> G

min :: G -> G -> G

Show G

Methods

showsPrec :: Int -> G -> ShowS

show :: G -> String

showList :: [G] -> ShowS

unG :: G -> Integer

data SPF

A Safe Prime Field (Zp): Q = large prime P = 2Q + 1, also prime G = generator for Zp order q

spfP :: SPF -> P

spfQ :: SPF -> Q

spfG :: SPF -> G

mkSPF :: MonadRandom m => Int -> m SPF

mkSPF' :: Integer -> Integer -> Integer -> Maybe SPF

type SPFM = ReaderT SPF

For computations using Safe Prime Field params

runSPFT :: SPF -> SPFM m a -> m a

runSPFM :: SPF -> SPFM Identity a -> a

gexpSafeSPF :: SPF -> Integer -> Integer

Compute g^e mod p

gexpSafeSPFM :: Monad m => Integer -> SPFM m Integer

expSafeSPF :: SPF -> Integer -> Integer -> Integer

Compute b^e mod p

expSafeSPFM :: Monad m => Integer -> Integer -> SPFM m Integer

randomInZq :: MonadRandom m => SPF -> m Integer

Generate random number in Zq

randomInZqM :: MonadRandom m => SPFM m Integer

randomInZp :: MonadRandom m => SPF -> m Integer

Generate random number in Zp

randomInZpM :: MonadRandom m => SPFM m Integer

modp :: SPF -> Integer -> Integer

modpM :: Monad m => Integer -> SPFM m Integer

(|*|) :: Monad m => SPFM m Integer -> SPFM m Integer -> SPFM m Integer

(|+|) :: Monad m => SPFM m Integer -> SPFM m Integer -> SPFM m Integer