-- 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 0.2


-- | ECC Standard Curves, taken from Standard Documents found somewhere(tm)
module Codec.Encryption.ECC.StandardCurves
data StandardCurve
StandardCurve :: Integer -> Integer -> Integer -> Integer -> Integer -> StandardCurve
stdc_p :: StandardCurve -> Integer
stdc_a :: StandardCurve -> Integer
stdc_b :: StandardCurve -> Integer
stdc_xp :: StandardCurve -> Integer
stdc_yp :: StandardCurve -> Integer
p521 :: StandardCurve
p256 :: StandardCurve


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

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

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

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

-- | given a generator and a curve, generate a point randomly
genkey :: ECP a => a -> EC -> IO a

-- | Elliptic Point Affine coordinates, two parameters x and y
data EPa
EPa :: (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 :: (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 :: (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 :: (Integer, Integer, Integer, Integer) -> EPmj
Infmj :: EPmj
instance Eq EPmj
instance Eq EPj
instance Eq EPp
instance Eq EPa
instance Eq EC
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