BrainpoolP320R1.hs

module Data.Curve.Weierstrass.BrainpoolP320R1
  ( module Data.Curve.Weierstrass
  , Point(..)
  -- * BrainpoolP320R1 curve
  , module Data.Curve.Weierstrass.BrainpoolP320R1
  ) where

import Protolude

import Data.Field.Galois
import GHC.Natural (Natural)

import Data.Curve.Weierstrass

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

-- | BrainpoolP320R1 curve.
data BrainpoolP320R1

-- | Field of points of BrainpoolP320R1 curve.
type Fq = Prime Q
type Q = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27

-- | Field of coefficients of BrainpoolP320R1 curve.
type Fr = Prime R
type R = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311

-- BrainpoolP320R1 curve is a Weierstrass curve.
instance Curve 'Weierstrass c BrainpoolP320R1 Fq Fr => WCurve c BrainpoolP320R1 Fq Fr where
  a_ = const _a
  {-# INLINABLE a_ #-}
  b_ = const _b
  {-# INLINABLE b_ #-}
  h_ = const _h
  {-# INLINABLE h_ #-}
  q_ = const _q
  {-# INLINABLE q_ #-}
  r_ = const _r
  {-# INLINABLE r_ #-}

-- | Affine BrainpoolP320R1 curve point.
type PA = WAPoint BrainpoolP320R1 Fq Fr

-- Affine BrainpoolP320R1 curve is a Weierstrass affine curve.
instance WACurve BrainpoolP320R1 Fq Fr where
  gA_ = gA
  {-# INLINABLE gA_ #-}

-- | Jacobian BrainpoolP320R1 point.
type PJ = WJPoint BrainpoolP320R1 Fq Fr

-- Jacobian BrainpoolP320R1 curve is a Weierstrass Jacobian curve.
instance WJCurve BrainpoolP320R1 Fq Fr where
  gJ_ = gJ
  {-# INLINABLE gJ_ #-}

-- | Projective BrainpoolP320R1 point.
type PP = WPPoint BrainpoolP320R1 Fq Fr

-- Projective BrainpoolP320R1 curve is a Weierstrass projective curve.
instance WPCurve BrainpoolP320R1 Fq Fr where
  gP_ = gP
  {-# INLINABLE gP_ #-}

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

-- | Coefficient @A@ of BrainpoolP320R1 curve.
_a :: Fq
_a = 0x3ee30b568fbab0f883ccebd46d3f3bb8a2a73513f5eb79da66190eb085ffa9f492f375a97d860eb4
{-# INLINABLE _a #-}

-- | Coefficient @B@ of BrainpoolP320R1 curve.
_b :: Fq
_b = 0x520883949dfdbc42d3ad198640688a6fe13f41349554b49acc31dccd884539816f5eb4ac8fb1f1a6
{-# INLINABLE _b #-}

-- | Cofactor of BrainpoolP320R1 curve.
_h :: Natural
_h = 0x1
{-# INLINABLE _h #-}

-- | Characteristic of BrainpoolP320R1 curve.
_q :: Natural
_q = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa6f6f40def4f92b9ec7893ec28fcd412b1f1b32e27
{-# INLINABLE _q #-}

-- | Order of BrainpoolP320R1 curve.
_r :: Natural
_r = 0xd35e472036bc4fb7e13c785ed201e065f98fcfa5b68f12a32d482ec7ee8658e98691555b44c59311
{-# INLINABLE _r #-}

-- | Coordinate @X@ of BrainpoolP320R1 curve.
_x :: Fq
_x = 0x43bd7e9afb53d8b85289bcc48ee5bfe6f20137d10a087eb6e7871e2a10a599c710af8d0d39e20611
{-# INLINABLE _x #-}

-- | Coordinate @Y@ of BrainpoolP320R1 curve.
_y :: Fq
_y = 0x14fdd05545ec1cc8ab4093247f77275e0743ffed117182eaa9c77877aaac6ac7d35245d1692e8ee1
{-# INLINABLE _y #-}

-- | Generator of affine BrainpoolP320R1 curve.
gA :: PA
gA = A _x _y
{-# INLINABLE gA #-}

-- | Generator of Jacobian BrainpoolP320R1 curve.
gJ :: PJ
gJ = J _x _y 1
{-# INLINABLE gJ #-}

-- | Generator of projective BrainpoolP320R1 curve.
gP :: PP
gP = P _x _y 1
{-# INLINABLE gP #-}