Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Base.Algebra.EllipticCurve.Ed25519

Contents

Orphan instances

Synopsis

data Ed25519 a
type Ed25519_Scalar = 7237005577332262213973186563042994240857116359379907606001950938285454250989
type Ed25519_Base = 57896044618658097711785492504343953926634992332820282019728792003956564819949
ed25519Add :: Point (Ed25519 Void) -> Point (Ed25519 Void) -> Point (Ed25519 Void)
ed25519Double :: Point (Ed25519 Void) -> Point (Ed25519 Void)

Documentation

data Ed25519 a Source #

The Ed25519 curve used in EdDSA signature scheme. a represents the "computational backend" used to store and perform operations on curve points.

Instances

Instances details

EllipticCurve (Ed25519 Void) Source #	The purely mathematical implementation of Ed25519. It is available for use as-is and serves as "backend" for the `UInt 256 (Zp p)` implementation as well.
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519 Associated Types type BaseField (Ed25519 Void) Source # type ScalarField (Ed25519 Void) Source # Methods inf :: Point (Ed25519 Void) Source # gen :: Point (Ed25519 Void) Source # add :: Point (Ed25519 Void) -> Point (Ed25519 Void) -> Point (Ed25519 Void) Source # mul :: ScalarField (Ed25519 Void) -> Point (Ed25519 Void) -> Point (Ed25519 Void) Source #
Finite (Zp p) => EllipticCurve (Ed25519 (Zp p) :: Type) Source #	Ed25519 with `UInt 256 (Zp p)` as computational backend
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Associated Types type BaseField (Ed25519 (Zp p)) Source # type ScalarField (Ed25519 (Zp p)) Source # Methods inf :: Point (Ed25519 (Zp p)) Source # gen :: Point (Ed25519 (Zp p)) Source # add :: Point (Ed25519 (Zp p)) -> Point (Ed25519 (Zp p)) -> Point (Ed25519 (Zp p)) Source # mul :: ScalarField (Ed25519 (Zp p)) -> Point (Ed25519 (Zp p)) -> Point (Ed25519 (Zp p)) Source #
(Arithmetic a, SymbolicData a (UInt 256 (ArithmeticCircuit a)), FromConstant Natural (UInt 512 (ArithmeticCircuit a)), EuclideanDomain (UInt 512 (ArithmeticCircuit a)), BinaryExpansion (UInt 256 (ArithmeticCircuit a))) => EllipticCurve (Ed25519 (ArithmeticCircuit a) :: Type) Source #	Ed25519 with `UInt 256 (ArithmeticCircuit a)` as computational backend
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Associated Types type BaseField (Ed25519 (ArithmeticCircuit a)) Source # type ScalarField (Ed25519 (ArithmeticCircuit a)) Source # Methods inf :: Point (Ed25519 (ArithmeticCircuit a)) Source # gen :: Point (Ed25519 (ArithmeticCircuit a)) Source # add :: Point (Ed25519 (ArithmeticCircuit a)) -> Point (Ed25519 (ArithmeticCircuit a)) -> Point (Ed25519 (ArithmeticCircuit a)) Source # mul :: ScalarField (Ed25519 (ArithmeticCircuit a)) -> Point (Ed25519 (ArithmeticCircuit a)) -> Point (Ed25519 (ArithmeticCircuit a)) Source #
SymbolicData a (UInt 256 (ArithmeticCircuit a)) => SymbolicData a (Point (Ed25519 (ArithmeticCircuit a))) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Methods pieces :: Point (Ed25519 (ArithmeticCircuit a)) -> [ArithmeticCircuit a] Source # restore :: [ArithmeticCircuit a] -> Point (Ed25519 (ArithmeticCircuit a)) Source # typeSize :: Natural Source #
(Ring a, Eq (Bool a) (BaseField (Ed25519 a))) => Eq (Bool a) (Point (Ed25519 a)) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Methods (==) :: Point (Ed25519 a) -> Point (Ed25519 a) -> Bool a Source # (/=) :: Point (Ed25519 a) -> Point (Ed25519 a) -> Bool a Source #
type BaseField (Ed25519 Void) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519 type BaseField (Ed25519 Void) = Zp Ed25519_Base
type BaseField (Ed25519 (Zp p) :: Type) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type BaseField (Ed25519 (Zp p) :: Type) = UInt 256 (Zp p)
type BaseField (Ed25519 (ArithmeticCircuit a) :: Type) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type BaseField (Ed25519 (ArithmeticCircuit a) :: Type) = UInt 256 (ArithmeticCircuit a)
type ScalarField (Ed25519 Void) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519 type ScalarField (Ed25519 Void) = Zp Ed25519_Scalar
type ScalarField (Ed25519 (Zp p) :: Type) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type ScalarField (Ed25519 (Zp p) :: Type) = UInt 256 (Zp p)
type ScalarField (Ed25519 (ArithmeticCircuit a) :: Type) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type ScalarField (Ed25519 (ArithmeticCircuit a) :: Type) = UInt 256 (ArithmeticCircuit a)

type Ed25519_Scalar = 7237005577332262213973186563042994240857116359379907606001950938285454250989 Source #

2^252 + 27742317777372353535851937790883648493 is the order of the multiplicative group in Ed25519 with the generator point defined below in instance EllipticCurve (Ed25519 Void)

type Ed25519_Base = 57896044618658097711785492504343953926634992332820282019728792003956564819949 Source #

2^255 - 19 is the order of the base field from which point coordinates are taken.

ed25519Add :: Point (Ed25519 Void) -> Point (Ed25519 Void) -> Point (Ed25519 Void) Source #

ed25519Double :: Point (Ed25519 Void) -> Point (Ed25519 Void) Source #

Orphan instances

Prime Ed25519_Base Source #
Instance details
Prime Ed25519_Scalar Source #
Instance details