/
BN254B.hs
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BN254B.hs
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module Data.Curve.Weierstrass.BN254B
( module Data.Curve.Weierstrass
, Point(..)
-- * BN254B curve
, module Data.Curve.Weierstrass.BN254B
) where
import Protolude
import Data.Field.Galois
import GHC.Natural (Natural)
import Data.Curve.Weierstrass
-------------------------------------------------------------------------------
-- Types
-------------------------------------------------------------------------------
-- | BN254B curve.
data BN254B
-- | Field of points of BN254B curve.
type Fq = Prime Q
type Q = 0x2523648240000001ba344d80000000086121000000000013a700000000000013
-- | Field of coefficients of BN254B curve.
type Fr = Prime R
type R = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d
-- BN254B curve is a Weierstrass curve.
instance Curve 'Weierstrass c BN254B Fq Fr => WCurve c BN254B 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 BN254B curve point.
type PA = WAPoint BN254B Fq Fr
-- Affine BN254B curve is a Weierstrass affine curve.
instance WACurve BN254B Fq Fr where
gA_ = gA
{-# INLINABLE gA_ #-}
-- | Jacobian BN254B point.
type PJ = WJPoint BN254B Fq Fr
-- Jacobian BN254B curve is a Weierstrass Jacobian curve.
instance WJCurve BN254B Fq Fr where
gJ_ = gJ
{-# INLINABLE gJ_ #-}
-- | Projective BN254B point.
type PP = WPPoint BN254B Fq Fr
-- Projective BN254B curve is a Weierstrass projective curve.
instance WPCurve BN254B Fq Fr where
gP_ = gP
{-# INLINABLE gP_ #-}
-------------------------------------------------------------------------------
-- Parameters
-------------------------------------------------------------------------------
-- | Coefficient @A@ of BN254B curve.
_a :: Fq
_a = 0x0
{-# INLINABLE _a #-}
-- | Coefficient @B@ of BN254B curve.
_b :: Fq
_b = 0x2
{-# INLINABLE _b #-}
-- | Cofactor of BN254B curve.
_h :: Natural
_h = 0x1
{-# INLINABLE _h #-}
-- | Characteristic of BN254B curve.
_q :: Natural
_q = 0x2523648240000001ba344d80000000086121000000000013a700000000000013
{-# INLINABLE _q #-}
-- | Order of BN254B curve.
_r :: Natural
_r = 0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d
{-# INLINABLE _r #-}
-- | Coordinate @X@ of BN254B curve.
_x :: Fq
_x = 0x2523648240000001ba344d80000000086121000000000013a700000000000012
{-# INLINABLE _x #-}
-- | Coordinate @Y@ of BN254B curve.
_y :: Fq
_y = 0x1
{-# INLINABLE _y #-}
-- | Generator of affine BN254B curve.
gA :: PA
gA = A _x _y
{-# INLINABLE gA #-}
-- | Generator of Jacobian BN254B curve.
gJ :: PJ
gJ = J _x _y 1
{-# INLINABLE gJ #-}
-- | Generator of projective BN254B curve.
gP :: PP
gP = P _x _y 1
{-# INLINABLE gP #-}