SECP521R1.hs

module Curve.Weierstrass.SECP521R1
  ( Fp
  , P
  , _a
  , _b
  , _g
  , _h
  , _n
  , _p
  ) where

import Protolude

import PrimeField (PrimeField)

import Curve.Weierstrass (Point(..), WCurve(..), WPoint)

-------------------------------------------------------------------------------
-- Types
-------------------------------------------------------------------------------

-- | SECP521R1 curve
data SECP521R1

-- | Field of SECP521R1 curve
type Fp = PrimeField 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

-- | SECP521R1 curve is a Weierstrass curve
instance WCurve SECP521R1 Fp where
  a_ = const _a
  {-# INLINE a_ #-}
  b_ = const _b
  {-# INLINE b_ #-}
  g_ = _g
  {-# INLINE g_ #-}

-- | Point of SECP521R1 curve
type P = WPoint SECP521R1 Fp

-------------------------------------------------------------------------------
-- Parameters
-------------------------------------------------------------------------------

-- | Coefficient @A@ of SECP521R1 curve
_a :: Fp
_a = 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc
{-# INLINE _a #-}

-- | Coefficient @B@ of SECP521R1 curve
_b :: Fp
_b = 0x51953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00
{-# INLINE _b #-}

-- | Generator of SECP521R1 curve
_g :: P
_g = A
     0xc6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66
     0x11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650
{-# INLINE _g #-}

-- | Cofactor of SECP521R1 curve
_h :: Integer
_h = 1
{-# INLINE _h #-}

-- | Order of SECP521R1 curve
_n :: Integer
_n = 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409
{-# INLINE _n #-}

-- | Characteristic of SECP521R1 curve
_p :: Integer
_p = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
{-# INLINE _p #-}