BLS12381.hs

module Curve.Weierstrass.BLS12381
  ( module Curve.Weierstrass
  , module Curve.Weierstrass.BLS12381
  , Point(..)
  ) where

import Protolude

import PrimeField

import Curve.Weierstrass

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

-- | BLS12381 curve.
data BLS12381

-- | Field of points of BLS12381 curve.
type Fq = PrimeField 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab

-- | Field of coefficients of BLS12381 curve.
type Fr = PrimeField 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001

-- | BLS12381 curve is a Weierstrass curve.
instance Curve 'Weierstrass c BLS12381 Fq Fr => WCurve c BLS12381 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_ #-}
  x_ = const _x
  {-# INLINABLE x_ #-}
  y_ = const _y
  {-# INLINABLE y_ #-}

-- | Affine BLS12381 curve point.
type PA = WAPoint BLS12381 Fq Fr

-- | Affine BLS12381 curve is a Weierstrass affine curve.
instance WACurve BLS12381 Fq Fr where
  gA_ = gA
  {-# INLINABLE gA_ #-}

-- | Jacobian BLS12381 point.
type PJ = WJPoint BLS12381 Fq Fr

-- | Jacobian BLS12381 curve is a Weierstrass Jacobian curve.
instance WJCurve BLS12381 Fq Fr where
  gJ_ = gJ
  {-# INLINABLE gJ_ #-}

-- | Projective BLS12381 point.
type PP = WPPoint BLS12381 Fq Fr

-- | Projective BLS12381 curve is a Weierstrass projective curve.
instance WPCurve BLS12381 Fq Fr where
  gP_ = gP
  {-# INLINABLE gP_ #-}

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

-- | Coefficient @A@ of BLS12381 curve.
_a :: Fq
_a = 0x0
{-# INLINABLE _a #-}

-- | Coefficient @B@ of BLS12381 curve.
_b :: Fq
_b = 0x4
{-# INLINABLE _b #-}

-- | Cofactor of BLS12381 curve.
_h :: Integer
_h = 0x396c8c005555e1568c00aaab0000aaab
{-# INLINABLE _h #-}

-- | Characteristic of BLS12381 curve.
_q :: Integer
_q = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
{-# INLINABLE _q #-}

-- | Order of BLS12381 curve.
_r :: Integer
_r = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
{-# INLINABLE _r #-}

-- | Coordinate @X@ of BLS12381 curve.
_x :: Fq
_x = 0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb
{-# INLINABLE _x #-}

-- | Coordinate @Y@ of BLS12381 curve.
_y :: Fq
_y = 0x8b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1
{-# INLINABLE _y #-}

-- | Generator of affine BLS12381 curve.
gA :: PA
gA = A _x _y
{-# INLINABLE gA #-}

-- | Generator of Jacobian BLS12381 curve.
gJ :: PJ
gJ = J _x _y 1
{-# INLINABLE gJ #-}

-- | Generator of projective BLS12381 curve.
gP :: PP
gP = P _x _y 1
{-# INLINABLE gP #-}