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SECT409R1.hs
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module Data.Curve.Binary.SECT409R1
( module Data.Curve.Binary
, Point(..)
-- * SECT409R1 curve
, module Data.Curve.Binary.SECT409R1
) where
import Protolude
import Data.Field.Galois
import GHC.Natural (Natural)
import Data.Curve.Binary
-------------------------------------------------------------------------------
-- Types
-------------------------------------------------------------------------------
-- | SECT409R1 curve.
data SECT409R1
-- | Field of points of SECT409R1 curve.
type F2m = Binary P
type P = 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
-- | Field of coefficients of SECT409R1 curve.
type Fr = Prime R
type R = 0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173
-- SECT409R1 curve is a binary curve.
instance Curve 'Binary c SECT409R1 F2m Fr => BCurve c SECT409R1 F2m Fr where
a_ = const _a
{-# INLINABLE a_ #-}
b_ = const _b
{-# INLINABLE b_ #-}
h_ = const _h
{-# INLINABLE h_ #-}
p_ = const _p
{-# INLINABLE p_ #-}
r_ = const _r
{-# INLINABLE r_ #-}
-- | Affine SECT409R1 curve point.
type PA = BAPoint SECT409R1 F2m Fr
-- Affine SECT409R1 curve is a binary affine curve.
instance BACurve SECT409R1 F2m Fr where
gA_ = gA
{-# INLINABLE gA_ #-}
-- | Projective SECT409R1 point.
type PP = BPPoint SECT409R1 F2m Fr
-- Projective SECT409R1 curve is a binary projective curve.
instance BPCurve SECT409R1 F2m Fr where
gP_ = gP
{-# INLINABLE gP_ #-}
-------------------------------------------------------------------------------
-- Parameters
-------------------------------------------------------------------------------
-- | Coefficient @A@ of SECT409R1 curve.
_a :: F2m
_a = 0x1
{-# INLINABLE _a #-}
-- | Coefficient @B@ of SECT409R1 curve.
_b :: F2m
_b = 0x21a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f
{-# INLINABLE _b #-}
-- | Cofactor of SECT409R1 curve.
_h :: Natural
_h = 0x2
{-# INLINABLE _h #-}
-- | Polynomial of SECT409R1 curve.
_p :: Natural
_p = 0x2000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001
{-# INLINABLE _p #-}
-- | Order of SECT409R1 curve.
_r :: Natural
_r = 0x10000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173
{-# INLINABLE _r #-}
-- | Coordinate @X@ of SECT409R1 curve.
_x :: F2m
_x = 0x15d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7
{-# INLINABLE _x #-}
-- | Coordinate @Y@ of SECT409R1 curve.
_y :: F2m
_y = 0x61b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706
{-# INLINABLE _y #-}
-- | Generator of affine SECT409R1 curve.
gA :: PA
gA = A _x _y
{-# INLINABLE gA #-}
-- | Generator of projective SECT409R1 curve.
gP :: PP
gP = P _x _y 1
{-# INLINABLE gP #-}