JubJub.hs

module Data.Curve.Edwards.JubJub
  ( module Data.Curve.Edwards
  , Point(..)
  -- * JubJub curve
  , module Data.Curve.Edwards.JubJub
  ) where

import Protolude

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

import Data.Curve.Edwards

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

-- | JubJub curve.
data JubJub

-- | Field of points of JubJub curve.
type Fq = Prime Q
type Q = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001

-- | Field of coefficients of JubJub curve.
type Fr = Prime R
type R = 0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7

-- JubJub curve is an Edwards curve.
instance Curve 'Edwards c JubJub Fq Fr => ECurve c JubJub 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 JubJub curve point.
type PA = EAPoint JubJub Fq Fr

-- Affine JubJub curve is an Edwards affine curve.
instance EACurve JubJub Fq Fr where
  gA_ = gA
  {-# INLINABLE gA_ #-}

-- | Projective JubJub point.
type PP = EPPoint JubJub Fq Fr

-- Projective JubJub curve is an Edwards projective curve.
instance EPCurve JubJub Fq Fr where
  gP_ = gP
  {-# INLINABLE gP_ #-}

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

-- | Coefficient @A@ of JubJub curve.
_a :: Fq
_a = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000
{-# INLINABLE _a #-}

-- | Coefficient @D@ of JubJub curve.
_d :: Fq
_d = 0x2a9318e74bfa2b48f5fd9207e6bd7fd4292d7f6d37579d2601065fd6d6343eb1
{-# INLINABLE _d #-}

-- | Cofactor of JubJub curve.
_h :: Natural
_h = 0x8
{-# INLINABLE _h #-}

-- | Characteristic of JubJub curve.
_q :: Natural
_q = 0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001
{-# INLINABLE _q #-}

-- | Order of JubJub curve.
_r :: Natural
_r = 0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7
{-# INLINABLE _r #-}

-- | Coordinate @X@ of JubJub curve.
_x :: Fq
_x = 0x5183972af8eff38ca624b4df00384882000c546bf2f39ede7f4ecf1a74f976c4
{-# INLINABLE _x #-}

-- | Coordinate @Y@ of JubJub curve.
_y :: Fq
_y = 0x3b43f8472ca2fc2c9e8fcc5abd9dc308096c8707ffa6833b146bad709349702e
{-# INLINABLE _y #-}

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

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