BLS12_381T.hs

module Curve.Weierstrass.BLS12_381T
  ( Fp2
  , P
  , _a
  , _b
  , _g
  , _h
  , _n
  , _p
  ) where

import Protolude

import ExtensionField (ExtensionField, IrreducibleMonic(..), fromList, x)

import Curve.Weierstrass (Point(..), WCurve(..), WPoint)
import Curve.Weierstrass.BLS12_381 (Fp)

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

-- | BLS12-381T curve
data BLS12_381T

-- | Field of BLS12-381T curve
data PolynomialU
instance IrreducibleMonic Fp PolynomialU where
  split _ = x ^ (2 :: Int) + 1
type Fp2 = ExtensionField Fp PolynomialU

-- | BLS12-381T curve is a Weierstrass curve
instance WCurve BLS12_381T Fp2 where
  a_ = const _a
  {-# INLINE a_ #-}
  b_ = const _b
  {-# INLINE b_ #-}
  g_ = _g
  {-# INLINE g_ #-}

-- | Point of BLS12-381T curve
type P = WPoint BLS12_381T Fp2

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

-- | Coefficient @A@ of BLS12-381T curve
_a :: Fp2
_a = 0
{-# INLINE _a #-}

-- | Coefficient @B@ of BLS12-381T curve
_b :: Fp2
_b = fromList [4, 4]
{-# INLINE _b #-}

-- | Generator of BLS12-381T curve
_g :: P
_g = A
  ( fromList
   [ 0x24aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8
   , 0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e
   ]
  )
  ( fromList
   [ 0xce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801
   , 0x606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be
   ]
  )
{-# INLINE _g #-}

-- | Cofactor of BLS12-381T curve
_h :: Integer
_h = 0x5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5
{-# INLINE _h #-}

-- | Order of BLS12-381T curve
_n :: Integer
_n = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
{-# INLINE _n #-}

-- | Characteristic of BLS12-381T curve
_p :: Integer
_p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
{-# INLINE _p #-}