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Ed3363.hs
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Ed3363.hs
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module Data.Curve.Edwards.Ed3363
( module Data.Curve.Edwards
, Point(..)
-- * Ed3363 curve
, module Data.Curve.Edwards.Ed3363
) where
import Protolude
import Data.Field.Galois
import GHC.Natural (Natural)
import Data.Curve.Edwards
-------------------------------------------------------------------------------
-- Types
-------------------------------------------------------------------------------
-- | Ed3363 curve.
data Ed3363
-- | Field of points of Ed3363 curve.
type Fq = Prime Q
type Q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd
-- | Field of coefficients of Ed3363 curve.
type Fr = Prime R
type R = 0x200000000000000000000000000000000000000000071415fa9850c0bd6b87f93baa7b2f95973e9fa805
-- Ed3363 curve is an Edwards curve.
instance Curve 'Edwards c Ed3363 Fq Fr => ECurve c Ed3363 Fq Fr where
a_ = const _a
{-# INLINABLE a_ #-}
d_ = const _d
{-# INLINABLE d_ #-}
h_ = const _h
{-# INLINABLE h_ #-}
q_ = const _q
{-# INLINABLE q_ #-}
r_ = const _r
{-# INLINABLE r_ #-}
-- | Affine Ed3363 curve point.
type PA = EAPoint Ed3363 Fq Fr
-- Affine Ed3363 curve is an Edwards affine curve.
instance EACurve Ed3363 Fq Fr where
gA_ = gA
{-# INLINABLE gA_ #-}
-- | Projective Ed3363 point.
type PP = EPPoint Ed3363 Fq Fr
-- Projective Ed3363 curve is an Edwards projective curve.
instance EPCurve Ed3363 Fq Fr where
gP_ = gP
{-# INLINABLE gP_ #-}
-------------------------------------------------------------------------------
-- Parameters
-------------------------------------------------------------------------------
-- | Coefficient @A@ of Ed3363 curve.
_a :: Fq
_a = 0x1
{-# INLINABLE _a #-}
-- | Coefficient @D@ of Ed3363 curve.
_d :: Fq
_d = 0x2b67
{-# INLINABLE _d #-}
-- | Cofactor of Ed3363 curve.
_h :: Natural
_h = 0x8
{-# INLINABLE _h #-}
-- | Characteristic of Ed3363 curve.
_q :: Natural
_q = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd
{-# INLINABLE _q #-}
-- | Order of Ed3363 curve.
_r :: Natural
_r = 0x200000000000000000000000000000000000000000071415fa9850c0bd6b87f93baa7b2f95973e9fa805
{-# INLINABLE _r #-}
-- | Coordinate @X@ of Ed3363 curve.
_x :: Fq
_x = 0xc
{-# INLINABLE _x #-}
-- | Coordinate @Y@ of Ed3363 curve.
_y :: Fq
_y = 0xc0dc616b56502e18e1c161d007853d1b14b46c3811c7ef435b6db5d5650ca0365db12bec68505fe8632
{-# INLINABLE _y #-}
-- | Generator of affine Ed3363 curve.
gA :: PA
gA = A _x _y
{-# INLINABLE gA #-}
-- | Generator of projective Ed3363 curve.
gP :: PP
gP = P _x _y 1
{-# INLINABLE gP #-}