module Data.Curve.Edwards.Ed25519
( module Data.Curve.Edwards
, Point(..)
, module Data.Curve.Edwards.Ed25519
) where
import Protolude
import Data.Field.Galois
import GHC.Natural (Natural)
import Data.Curve.Edwards
data Ed25519
type Fq = Prime Q
type Q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed
type Fr = Prime R
type R = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
instance Curve 'Edwards c Ed25519 Fq Fr => ECurve c Ed25519 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_ #-}
type PA = EAPoint Ed25519 Fq Fr
instance EACurve Ed25519 Fq Fr where
gA_ = gA
{-# INLINABLE gA_ #-}
type PP = EPPoint Ed25519 Fq Fr
instance EPCurve Ed25519 Fq Fr where
gP_ = gP
{-# INLINABLE gP_ #-}
_a :: Fq
_a = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec
{-# INLINABLE _a #-}
_d :: Fq
_d = 0x52036cee2b6ffe738cc740797779e89800700a4d4141d8ab75eb4dca135978a3
{-# INLINABLE _d #-}
_h :: Natural
_h = 0x8
{-# INLINABLE _h #-}
_q :: Natural
_q = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed
{-# INLINABLE _q #-}
_r :: Natural
_r = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
{-# INLINABLE _r #-}
_x :: Fq
_x = 0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a
{-# INLINABLE _x #-}
_y :: Fq
_y = 0x6666666666666666666666666666666666666666666666666666666666666658
{-# INLINABLE _y #-}
gA :: PA
gA = A _x _y
{-# INLINABLE gA #-}
gP :: PP
gP = P _x _y 1
{-# INLINABLE gP #-}