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BrainpoolP224R1.hs
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/
BrainpoolP224R1.hs
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module Data.Curve.Weierstrass.BrainpoolP224R1
( module Data.Curve.Weierstrass
, Point(..)
-- * BrainpoolP224R1 curve
, module Data.Curve.Weierstrass.BrainpoolP224R1
) where
import Protolude
import Data.Field.Galois
import GHC.Natural (Natural)
import Data.Curve.Weierstrass
-------------------------------------------------------------------------------
-- Types
-------------------------------------------------------------------------------
-- | BrainpoolP224R1 curve.
data BrainpoolP224R1
-- | Field of points of BrainpoolP224R1 curve.
type Fq = Prime Q
type Q = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff
-- | Field of coefficients of BrainpoolP224R1 curve.
type Fr = Prime R
type R = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f
-- BrainpoolP224R1 curve is a Weierstrass curve.
instance Curve 'Weierstrass c BrainpoolP224R1 Fq Fr => WCurve c BrainpoolP224R1 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 BrainpoolP224R1 curve point.
type PA = WAPoint BrainpoolP224R1 Fq Fr
-- Affine BrainpoolP224R1 curve is a Weierstrass affine curve.
instance WACurve BrainpoolP224R1 Fq Fr where
gA_ = gA
{-# INLINABLE gA_ #-}
-- | Jacobian BrainpoolP224R1 point.
type PJ = WJPoint BrainpoolP224R1 Fq Fr
-- Jacobian BrainpoolP224R1 curve is a Weierstrass Jacobian curve.
instance WJCurve BrainpoolP224R1 Fq Fr where
gJ_ = gJ
{-# INLINABLE gJ_ #-}
-- | Projective BrainpoolP224R1 point.
type PP = WPPoint BrainpoolP224R1 Fq Fr
-- Projective BrainpoolP224R1 curve is a Weierstrass projective curve.
instance WPCurve BrainpoolP224R1 Fq Fr where
gP_ = gP
{-# INLINABLE gP_ #-}
-------------------------------------------------------------------------------
-- Parameters
-------------------------------------------------------------------------------
-- | Coefficient @A@ of BrainpoolP224R1 curve.
_a :: Fq
_a = 0x68a5e62ca9ce6c1c299803a6c1530b514e182ad8b0042a59cad29f43
{-# INLINABLE _a #-}
-- | Coefficient @B@ of BrainpoolP224R1 curve.
_b :: Fq
_b = 0x2580f63ccfe44138870713b1a92369e33e2135d266dbb372386c400b
{-# INLINABLE _b #-}
-- | Cofactor of BrainpoolP224R1 curve.
_h :: Natural
_h = 0x1
{-# INLINABLE _h #-}
-- | Characteristic of BrainpoolP224R1 curve.
_q :: Natural
_q = 0xd7c134aa264366862a18302575d1d787b09f075797da89f57ec8c0ff
{-# INLINABLE _q #-}
-- | Order of BrainpoolP224R1 curve.
_r :: Natural
_r = 0xd7c134aa264366862a18302575d0fb98d116bc4b6ddebca3a5a7939f
{-# INLINABLE _r #-}
-- | Coordinate @X@ of BrainpoolP224R1 curve.
_x :: Fq
_x = 0xd9029ad2c7e5cf4340823b2a87dc68c9e4ce3174c1e6efdee12c07d
{-# INLINABLE _x #-}
-- | Coordinate @Y@ of BrainpoolP224R1 curve.
_y :: Fq
_y = 0x58aa56f772c0726f24c6b89e4ecdac24354b9e99caa3f6d3761402cd
{-# INLINABLE _y #-}
-- | Generator of affine BrainpoolP224R1 curve.
gA :: PA
gA = A _x _y
{-# INLINABLE gA #-}
-- | Generator of Jacobian BrainpoolP224R1 curve.
gJ :: PJ
gJ = J _x _y 1
{-# INLINABLE gJ #-}
-- | Generator of projective BrainpoolP224R1 curve.
gP :: PP
gP = P _x _y 1
{-# INLINABLE gP #-}