BLS48581T.hs

module Data.Curve.Weierstrass.BLS48581T
  ( module Data.Curve.Weierstrass
  , Point(..)
  -- * BLS48581 curve
  , module Data.Curve.Weierstrass.BLS48581T
  ) where

import Protolude

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

import Data.Curve.Weierstrass
import Data.Curve.Weierstrass.BLS48581 (BLS48581, Fq, Fr)

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

-- | Field of points of BLS48581 curve over @Fq2@.
type Fq2 = Extension U Fq
data U
instance IrreducibleMonic U Fq where
  poly _ = [1, 0, 1]
  {-# INLINABLE poly #-}
-- | Field of points of BLS48581 curve over @Fq4@.
type Fq4 = Extension V Fq2
data V
instance IrreducibleMonic V Fq2 where
  poly _ = [U + 1, 0, 1]
  {-# INLINABLE poly #-}
-- | Field of points of BLS48581 curve over @Fq8@.
type Fq8 = Extension W Fq4
data W
instance IrreducibleMonic W Fq4 where
  poly _ = [U, 0, 1]
  {-# INLINABLE poly #-}

-- BLS48581 curve is a Weierstrass curve.
instance Curve 'Weierstrass c BLS48581 Fq8 Fr => WCurve c BLS48581 Fq8 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 BLS48581 curve point.
type PA = WAPoint BLS48581 Fq8 Fr

-- Affine BLS48581 curve is a Weierstrass affine curve.
instance WACurve BLS48581 Fq8 Fr where
  gA_ = gA
  {-# INLINABLE gA_ #-}

-- | Jacobian BLS48581 point.
type PJ = WJPoint BLS48581 Fq8 Fr

-- Jacobian BLS48581 curve is a Weierstrass Jacobian curve.
instance WJCurve BLS48581 Fq8 Fr where
  gJ_ = gJ
  {-# INLINABLE gJ_ #-}

-- | Projective BLS48581 point.
type PP = WPPoint BLS48581 Fq8 Fr

-- Projective BLS48581 curve is a Weierstrass projective curve.
instance WPCurve BLS48581 Fq8 Fr where
  gP_ = gP
  {-# INLINABLE gP_ #-}

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

-- | Coefficient @A@ of BLS48581 curve.
_a :: Fq8
_a = toE' [
          ]
{-# INLINABLE _a #-}

-- | Coefficient @B@ of BLS48581 curve.
_b :: Fq8
_b = toE' [ toE' [
                 ]
          , toE' [ toE' [
                        ]
                 , toE' [ 0x9407b9ff9a3b7989c12718ea38095002b7427c6891098dd9df36078f9cbaa225245721d7b7041566ce6981ca7a39b6d7b41b3d2a898b877052bc7efb90d2524561f6e0aa732b2c895
                        , 0x9407b9ff9a3b7989c12718ea38095002b7427c6891098dd9df36078f9cbaa225245721d7b7041566ce6981ca7a39b6d7b41b3d2a898b877052bc7efb90d2524561f6e0aa732b2c896
                        ]
                 ]
          ]
{-# INLINABLE _b #-}

-- | Cofactor of BLS48581 curve.
_h :: Natural
_h = 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
{-# INLINABLE _h #-}

-- | Characteristic of BLS48581 curve.
_q :: Natural
_q = 0x1280f73ff3476f313824e31d47012a0056e84f8d122131bb3be6c0f1f3975444a48ae43af6e082acd9cd30394f4736daf68367a5513170ee0a578fdf721a4a48ac3edc154e6565912b
{-# INLINABLE _q #-}

-- | Order of BLS48581 curve.
_r :: Natural
_r = 0x2386f8a925e2885e233a9ccc1615c0d6c635387a3f0b3cbe003fad6bc972c2e6e741969d34c4c92016a85c7cd0562303c4ccbe599467c24da118a5fe6fcd671c01
{-# INLINABLE _r #-}

-- | Coordinate @X@ of BLS48581 curve.
_x :: Fq8
_x = toE' [ toE' [ toE' [ 0x5d615d9a7871e4a38237fa45a2775debabbefc70344dbccb7de64db3a2ef156c46ff79baad1a8c42281a63ca0612f400503004d80491f510317b79766322154dec34fd0b4ace8bfab
                        , 0x7c4973ece2258512069b0e86abc07e8b22bb6d980e1623e9526f6da12307f4e1c3943a00abfedf16214a76affa62504f0c3c7630d979630ffd75556a01afa143f1669b36676b47c57
                        ]
                 , toE' [ 0x1fccc70198f1334e1b2ea1853ad83bc73a8a6ca9ae237ca7a6d6957ccbab5ab6860161c1dbd19242ffae766f0d2a6d55f028cbdfbb879d5fea8ef4cded6b3f0b46488156ca55a3e6a
                        , 0xbe2218c25ceb6185c78d8012954d4bfe8f5985ac62f3e5821b7b92a393f8be0cc218a95f63e1c776e6ec143b1b279b9468c31c5257c200ca52310b8cb4e80bc3f09a7033cbb7feafe
                        ]
                 ]
          , toE' [ toE' [ 0x38b91c600b35913a3c598e4caa9dd63007c675d0b1642b5675ff0e7c5805386699981f9e48199d5ac10b2ef492ae589274fad55fc1889aa80c65b5f746c9d4cbb739c3a1c53f8cce5
                        , 0xc96c7797eb0738603f1311e4ecda088f7b8f35dcef0977a3d1a58677bb037418181df63835d28997eb57b40b9c0b15dd7595a9f177612f097fc7960910fce3370f2004d914a3c093a
                        ]
                 , toE' [ 0xb9b7951c6061ee3f0197a498908aee660dea41b39d13852b6db908ba2c0b7a449cef11f293b13ced0fd0caa5efcf3432aad1cbe4324c22d63334b5b0e205c3354e41607e60750e057
                        , 0x827d5c22fb2bdec5282624c4f4aaa2b1e5d7a9defaf47b5211cf741719728a7f9f8cfca93f29cff364a7190b7e2b0d4585479bd6aebf9fc44e56af2fc9e97c3f84e19da00fbc6ae34
                        ]
                 ]
          ]
{-# INLINABLE _x #-}

-- | Coordinate @Y@ of BLS48581 curve.
_y :: Fq8
_y = toE' [ toE' [ toE' [ 0xeb53356c375b5dfa497216452f3024b918b4238059a577e6f3b39ebfc435faab0906235afa27748d90f7336d8ae5163c1599abf77eea6d659045012ab12c0ff323edd3fe4d2d7971
                        , 0x284dc75979e0ff144da6531815fcadc2b75a422ba325e6fba01d72964732fcbf3afb096b243b1f192c5c3d1892ab24e1dd212fa097d760e2e588b423525ffc7b111471db936cd5665
                        ]
                 , toE' [ 0xb36a201dd008523e421efb70367669ef2c2fc5030216d5b119d3a480d370514475f7d5c99d0e90411515536ca3295e5e2f0c1d35d51a652269cbc7c46fc3b8fde68332a526a2a8474
                        , 0xaec25a4621edc0688223fbbd478762b1c2cded3360dcee23dd8b0e710e122d2742c89b224333fa40dced2817742770ba10d67bda503ee5e578fb3d8b8a1e5337316213da92841589d
                        ]
                 ]
          , toE' [ toE' [ 0xd209d5a223a9c46916503fa5a88325a2554dc541b43dd93b5a959805f1129857ed85c77fa238cdce8a1e2ca4e512b64f59f430135945d137b08857fdddfcf7a43f47831f982e50137
                        , 0x7d0d03745736b7a513d339d5ad537b90421ad66eb16722b589d82e2055ab7504fa83420e8c270841f6824f47c180d139e3aafc198caa72b679da59ed8226cf3a594eedc58cf90bee4
                        ]
                 , toE' [ 0x896767811be65ea25c2d05dfdd17af8a006f364fc0841b064155f14e4c819a6df98f425ae3a2864f22c1fab8c74b2618b5bb40fa639f53dccc9e884017d9aa62b3d41faeafeb23986
                        , 0x35e2524ff89029d393a5c07e84f981b5e068f1406be8e50c87549b6ef8eca9a9533a3f8e69c31e97e1ad0333ec719205417300d8c4ab33f748e5ac66e84069c55d667ffcb732718b6
                        ]
                 ]
          ]
{-# INLINABLE _y #-}

-- | Generator of affine BLS48581 curve.
gA :: PA
gA = A _x _y
{-# INLINABLE gA #-}

-- | Generator of Jacobian BLS48581 curve.
gJ :: PJ
gJ = J _x _y 1
{-# INLINABLE gJ #-}

-- | Generator of projective BLS48581 curve.
gP :: PP
gP = P _x _y 1
{-# INLINABLE gP #-}