-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Elliptic Curve Cryptography for Haskell
--   
--   Pure math & algorithms for Elliptic Curve Cryptography in Haskell
@package hecc
@version 0.3.3


-- | ECC Standard Curves, taken from Standard Documents found somewhere(tm)
module Codec.Crypto.ECC.StandardCurves
data StandardCurve
StandardCurve :: Int -> Integer -> Integer -> Integer -> Integer -> Integer -> StandardCurve
stdc_l :: StandardCurve -> Int
stdc_p :: StandardCurve -> Integer
stdc_a :: StandardCurve -> Integer
stdc_b :: StandardCurve -> Integer
stdc_xp :: StandardCurve -> Integer
stdc_yp :: StandardCurve -> Integer
p521 :: StandardCurve
p256 :: StandardCurve
p384 :: StandardCurve
data StandardCurveF2
StandardCurveF2 :: Int -> F2 -> F2 -> F2 -> F2 -> F2 -> StandardCurveF2
stdcF_l :: StandardCurveF2 -> Int
stdcF_p :: StandardCurveF2 -> F2
stdcF_a :: StandardCurveF2 -> F2
stdcF_b :: StandardCurveF2 -> F2
stdcF_xp :: StandardCurveF2 -> F2
stdcF_yp :: StandardCurveF2 -> F2
k283 :: StandardCurveF2
b283 :: StandardCurveF2


-- | ECC Base algorithms & point formats
module Codec.Crypto.ECC.Base

-- | class of all Elliptic Curve Points
class ECP a
inf :: ECP a => a
fromAffineCoords :: ECP a => EPa -> a
getBitLength :: ECP a => a -> Int
getCurve :: ECP a => a -> EC
getx :: ECP a => a -> Integer
gety :: ECP a => a -> Integer
pdouble :: ECP a => a -> a
padd :: ECP a => a -> a -> a

-- | class of all Elliptic Curves, has the form y^2=x^3+A*x+B mod P, the
--   parameters being A, B and P
data EC
EC :: (Integer, Integer, Integer) -> EC

-- | computing the modular inverse of <tt>a</tt> <a>mod</a> <tt>m</tt>
modinv :: Integral a => a -> a -> a

-- | this is a generic handle for Point Multiplication. The implementation
--   may change.
pmul :: ECP a => a -> Integer -> a

-- | generic verify, if generic ECP is on EC via getx and gety
ison :: ECP a => a -> Bool
binary :: Integer -> String

-- | Elliptic Point Affine coordinates, two parameters x and y
data EPa
EPa :: (BitLength, EC, Integer, Integer) -> EPa
Infa :: EPa

-- | Elliptic Point Projective coordinates, three parameters x, y and z,
--   like affine (x<i>z,y</i>z)
data EPp
EPp :: (BitLength, EC, Integer, Integer, Integer) -> EPp
Infp :: EPp

-- | Elliptic Point Jacobian coordinates, three parameter x, y and z, like
--   affine (x<i>z^2,y</i>z^3)
data EPj
EPj :: (BitLength, EC, Integer, Integer, Integer) -> EPj
Infj :: EPj

-- | Elliptic Point Modified Jacobian coordinates, four parameters x,y,z
--   and A*z^4 (A being the first curve-parameter), like affine coordinates
--   (x<i>z^2,y</i>z^3)
data EPmj
EPmj :: (BitLength, EC, Integer, Integer, Integer, Integer) -> EPmj
Infmj :: EPmj
p256point :: ECP a => a
p384point :: ECP a => a
p521point :: ECP a => a

-- | class of all Elliptic Curve Points
class ECPF2 a
infF2 :: ECPF2 a => a
fromAffineCoordsF2 :: ECPF2 a => EPaF2 -> a
getBitLengthF2 :: ECPF2 a => a -> BitLength
getCurveF2 :: ECPF2 a => a -> ECSC
getxF2 :: ECPF2 a => a -> F2
getyF2 :: ECPF2 a => a -> F2
pdoubleF2 :: ECPF2 a => a -> a
paddF2 :: ECPF2 a => a -> a -> a

-- | All Elliptic Curves, binary
class ECurve a
getA :: ECurve a => a -> F2
getB :: ECurve a => a -> F2
getP :: ECurve a => a -> F2

-- | class of (non-hyper) Elliptic Curves, has the form y^2+x*y=x^3+A*x^2+B
--   mod P, the parameters being A, B and P
data ECSC
ECSC :: (F2, F2, F2) -> ECSC

-- | computing the modular inverse of <tt>a</tt> <tt>emod</tt> <tt>m</tt>
modinvF2K :: ECPF2 a => a -> a

-- | this is a generic handle for Point Multiplication. The implementation
--   may change.
pmulF2 :: ECPF2 a => a -> Integer -> ECPF2 a => a

-- | generic verify, if generic ECP is on EC via getx and gety
isonF2 :: (ECPF2 a, Eq a) => a -> Bool

-- | Elliptic Point Affine coordinates, two parameters x and y
data EPaF2
EPaF2 :: (BitLength, ECSC, F2, F2) -> EPaF2
InfaF2 :: EPaF2

-- | Elliptic Point Projective coordinates, three parameters x, y and z,
--   like affine (x<i>z,y</i>z)
data EPpF2
EPpF2 :: (BitLength, ECSC, F2, F2, F2) -> EPpF2
InfpF2 :: EPpF2
b283point :: ECPF2 a => a
k283point :: ECPF2 a => a
instance Eq EC
instance Eq EPa
instance Eq EPp
instance Eq EPj
instance Eq EPmj
instance Eq ECSC
instance Eq EPaF2
instance Eq EPpF2
instance ECPF2 EPpF2
instance Show EPpF2
instance ECPF2 EPaF2
instance Show EPaF2
instance ECurve ECSC
instance Show ECSC
instance ECP EPmj
instance Show EPmj
instance ECP EPj
instance Show EPj
instance ECP EPp
instance Show EPp
instance ECP EPa
instance Show EPa
instance Show EC