Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Base.Algebra.EllipticCurve.Ed25519

Contents

Orphan instances

Synopsis

data Ed25519 c
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 c Source #

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

Instances

Instances details

(Symbolic c, NFData (c (Vector Size))) => EllipticCurve (Ed25519 c :: Type) Source #	Ed25519 with `UInt 256 ArithmeticCircuit a` as computational backend
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Associated Types type BaseField (Ed25519 c) Source # type ScalarField (Ed25519 c) Source # Methods inf :: Point (Ed25519 c) Source # gen :: Point (Ed25519 c) Source # add :: Point (Ed25519 c) -> Point (Ed25519 c) -> Point (Ed25519 c) Source # mul :: ScalarField (Ed25519 c) -> Point (Ed25519 c) -> Point (Ed25519 c) Source #
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 #
(KnownNat n, Symbolic c, NFData (c (Vector Size))) => PedersonSetup n (Point (Ed25519 c)) Source #
Instance details Defined in ZkFold.Base.Protocol.Protostar.Commit Methods groupElements :: Vector n (Point (Ed25519 c)) Source #
Symbolic c => Eq (Bool c) (Point (Ed25519 c)) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Methods (==) :: Point (Ed25519 c) -> Point (Ed25519 c) -> Bool c Source # (/=) :: Point (Ed25519 c) -> Point (Ed25519 c) -> Bool c Source #
(Symbolic c, BaseField c ~ a) => SymbolicData (Point (Ed25519 c)) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Associated Types type Context (Point (Ed25519 c)) :: (Type -> Type) -> Type Source # type Support (Point (Ed25519 c)) Source # type Layout (Point (Ed25519 c)) :: Type -> Type Source # type Payload (Point (Ed25519 c)) :: Type -> Type Source # Methods arithmetize :: Point (Ed25519 c) -> Support (Point (Ed25519 c)) -> Context (Point (Ed25519 c)) (Layout (Point (Ed25519 c))) Source # payload :: Point (Ed25519 c) -> Support (Point (Ed25519 c)) -> Payload (Point (Ed25519 c)) (WitnessField (Context (Point (Ed25519 c)))) Source # restore :: Context (Point (Ed25519 c)) ~ c0 => (Support (Point (Ed25519 c)) -> (c0 (Layout (Point (Ed25519 c))), Payload (Point (Ed25519 c)) (WitnessField c0))) -> Point (Ed25519 c) Source #
type BaseField (Ed25519 c :: Type) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type BaseField (Ed25519 c :: Type) = FFA Ed25519_Base c
type BaseField (Ed25519 Void) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519 type BaseField (Ed25519 Void) = Zp Ed25519_Base
type ScalarField (Ed25519 c :: Type) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type ScalarField (Ed25519 c :: Type) = FieldElement c
type ScalarField (Ed25519 Void) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519 type ScalarField (Ed25519 Void) = Zp Ed25519_Scalar
type Context (Point (Ed25519 c)) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type Context (Point (Ed25519 c)) = c
type Layout (Point (Ed25519 c)) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type Layout (Point (Ed25519 c)) = Layout (FFA Ed25519_Base c, FFA Ed25519_Base c)
type Payload (Point (Ed25519 c)) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type Payload (Point (Ed25519 c)) = Payload (FFA Ed25519_Base c, FFA Ed25519_Base c)
type Support (Point (Ed25519 c)) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 type Support (Point (Ed25519 c)) = Support (FFA Ed25519_Base c)

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 r)

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