ZkFold.Base.Algebra.EllipticCurve.Ed25519

Documentation

data Ed25519

The Ed25519 curve used in EdDSA signature scheme.

Instances

EllipticCurve Ed25519

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.

Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519

Associated Types

type BaseField Ed25519

type ScalarField Ed25519

type BooleanOf Ed25519

Methods

pointGen :: Point Ed25519

add :: Point Ed25519 -> Point Ed25519 -> Point Ed25519

mul :: ScalarField Ed25519 -> Point Ed25519 -> Point Ed25519

type BaseField Ed25519

Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519

type BaseField Ed25519 = Zp Ed25519_Base

type BooleanOf Ed25519

Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519

type BooleanOf Ed25519 = Bool

type ScalarField Ed25519

Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519

type ScalarField Ed25519 = Zp Ed25519_Scalar

type Ed25519_Scalar = 7237005577332262213973186563042994240857116359379907606001950938285454250989

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

type Ed25519_Base = 57896044618658097711785492504343953926634992332820282019728792003956564819949

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

ed25519Add :: Point Ed25519 -> Point Ed25519 -> Point Ed25519

ed25519Double :: Point Ed25519 -> Point Ed25519

Orphan instances

Prime Ed25519_Base

Prime Ed25519_Scalar