Curve448.hs

module Curve.Montgomery.Curve448
  ( Fp
  , P
  , _a
  , _b
  , _g
  , _h
  , _n
  , _p
  ) where

import Protolude

import PrimeField (PrimeField)

import Curve.Montgomery (Point(..), MCurve(..), MPoint)

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

-- | Curve448 curve
data Curve448

-- | Field of Curve448 curve
type Fp = PrimeField 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff

-- | Curve448 curve is a Montgomery curve
instance MCurve Curve448 Fp where
  a_ = const _a
  {-# INLINE a_ #-}
  b_ = const _b
  {-# INLINE b_ #-}
  g_ = _g
  {-# INLINE g_ #-}

-- | Point of Curve448 curve
type P = MPoint Curve448 Fp

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

-- | Coefficient @A@ of Curve448 curve
_a :: Fp
_a = 0x262a6
{-# INLINE _a #-}

-- | Coefficient @B@ of Curve448 curve
_b :: Fp
_b = 1
{-# INLINE _b #-}

-- | Generator of Curve448 curve
_g :: P
_g = A
     5
     0x7d235d1295f5b1f66c98ab6e58326fcecbae5d34f55545d060f75dc28df3f6edb8027e2346430d211312c4b150677af76fd7223d457b5b1a
{-# INLINE _g #-}

-- | Cofactor of Curve448 curve
_h :: Integer
_h = 4
{-# INLINE _h #-}

-- | Order of Curve448 curve
_n :: Integer
_n = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3
{-# INLINE _n #-}

-- | Characteristic of Curve448 curve
_p :: Integer
_p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff
{-# INLINE _p #-}