{-# LANGUAGE DerivingVia          #-}
{-# LANGUAGE OverloadedLists      #-}
{-# LANGUAGE TypeOperators        #-}
{-# LANGUAGE UndecidableInstances #-}
{-# OPTIONS_GHC -Wno-orphans #-}

module ZkFold.Base.Algebra.EllipticCurve.PlutoEris
 ( PlutoEris_p
 , PlutoEris_q
 , Pluto_Point
 , Eris_Point
 , Triton_Point
 ) where

import           ZkFold.Base.Algebra.Basic.Class
import           ZkFold.Base.Algebra.Basic.Field
import           ZkFold.Base.Algebra.Basic.Number
import           ZkFold.Base.Algebra.EllipticCurve.Class
import           ZkFold.Base.Algebra.Polynomials.Univariate (toPoly)

-- Designations of curve parameters are as in:
-- https://github.com/daira/pluto-eris

-------------------------- Pluto/Eris curves -------------------------

type PlutoEris_p = 0x24000000000024000130e0000d7f70e4a803ca76f439266f443f9a5cda8a6c7be4a7a5fe8fadffd6a2a7e8c30006b9459ffffcd300000001
instance Prime PlutoEris_p

type PlutoEris_q = 0x24000000000024000130e0000d7f70e4a803ca76f439266f443f9a5c7a8a6c7be4a775fe8e177fd69ca7e85d60050af41ffffcd300000001
instance Prime PlutoEris_q

instance Field field => WeierstrassCurve "Pluto-Eris" field where
  weierstrassB :: field
weierstrassB = Nat -> field
forall a b. FromConstant a b => a -> b
fromConstant (Nat
57 :: Natural)

type Pluto_Point = Weierstrass "Pluto-Eris" (Point (Zp PlutoEris_p))
instance CyclicGroup Pluto_Point where
  type ScalarFieldOf Pluto_Point = Zp PlutoEris_q
  pointGen :: Pluto_Point
pointGen = Zp PlutoEris_p -> Zp PlutoEris_p -> Pluto_Point
forall field point. Planar field point => field -> field -> point
pointXY (-Zp PlutoEris_p
2) Zp PlutoEris_p
7
instance Scale (Zp PlutoEris_q) Pluto_Point where
  scale :: Zp PlutoEris_q -> Pluto_Point -> Pluto_Point
scale Zp PlutoEris_q
n = Nat -> Pluto_Point -> Pluto_Point
forall b a. Scale b a => b -> a -> a
scale (Zp PlutoEris_q -> Const (Zp PlutoEris_q)
forall a. ToConstant a => a -> Const a
toConstant Zp PlutoEris_q
n)

type Eris_Point = Weierstrass "Pluto-Eris" (Point (Zp PlutoEris_q))
instance CyclicGroup Eris_Point where
  type ScalarFieldOf Eris_Point = Zp PlutoEris_p
  pointGen :: Eris_Point
pointGen = Zp PlutoEris_q -> Zp PlutoEris_q -> Eris_Point
forall field point. Planar field point => field -> field -> point
pointXY (-Zp PlutoEris_q
2) Zp PlutoEris_q
7
instance Scale (Zp PlutoEris_p) Eris_Point where
  scale :: Zp PlutoEris_p -> Eris_Point -> Eris_Point
scale Zp PlutoEris_p
n = Nat -> Eris_Point -> Eris_Point
forall b a. Scale b a => b -> a -> a
scale (Zp PlutoEris_p -> Const (Zp PlutoEris_p)
forall a. ToConstant a => a -> Const a
toConstant Zp PlutoEris_p
n)

-------------------------- Triton curve ----------------------------

-- The definition of Triton has not been finalized and is subject to change

instance IrreduciblePoly (Zp PlutoEris_p) "i*sqrt5" where
  irreduciblePoly :: Poly (Zp PlutoEris_p)
irreduciblePoly = Vector (Zp PlutoEris_p) -> Poly (Zp PlutoEris_p)
forall c. (Ring c, Eq c) => Vector c -> Poly c
toPoly [Item (Vector (Zp PlutoEris_p))
Zp PlutoEris_p
5, Item (Vector (Zp PlutoEris_p))
Zp PlutoEris_p
0, Item (Vector (Zp PlutoEris_p))
Zp PlutoEris_p
1]

instance WeierstrassCurve "Triton" (Ext2 (Zp PlutoEris_p) "i*sqrt5") where
  weierstrassB :: Ext2 (Zp PlutoEris_p) "i*sqrt5"
weierstrassB = Zp PlutoEris_p -> Zp PlutoEris_p -> Ext2 (Zp PlutoEris_p) "i*sqrt5"
forall f (e :: Symbol). f -> f -> Ext2 f e
Ext2 Zp PlutoEris_p
3 Zp PlutoEris_p
1

type Triton_Point =
  Weierstrass "Triton" (Point (Ext2 (Zp PlutoEris_p) "i*sqrt5"))