Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Base.Algebra.EllipticCurve.Class

Documentation

data Point (curve :: Type) Source #

Constructors

Point
Fields _x :: BaseField curve _y :: BaseField curve _isInf :: BooleanOf curve

Instances

Instances details

(EllipticCurve curve, Random (ScalarField curve)) => PedersonSetup List (Point curve :: Type) Source #
Instance details Defined in ZkFold.Base.Protocol.IVC.Commit Methods groupElements :: [Point curve] Source #
(PedersonSetup s (Point curve), Functor s) => PedersonSetup (s :: Type -> Type) (Constant (Point curve) a :: Type) Source #
Instance details Defined in ZkFold.Base.Protocol.IVC.Commit Methods groupElements :: s (Constant (Point curve) a) Source #
(EllipticCurve curve, AdditiveGroup (BaseField curve)) => Scale Integer (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods scale :: Integer -> Point curve -> Point curve Source #
EllipticCurve curve => Scale Natural (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods scale :: Natural -> Point curve -> Point curve Source #
(EllipticCurve curve, BooleanOf curve ~ Bool, Eq s, BinaryExpansion s, Bits s ~ [s]) => Scale s (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods scale :: s -> Point curve -> Point curve Source #
(field ~ BaseField curve, bool ~ BooleanOf curve, BoolType bool) => Planar field (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods pointXY :: field -> field -> Point curve Source #
(EllipticCurve curve, bool ~ BooleanOf curve) => Conditional bool (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods bool :: Point curve -> Point curve -> bool -> Point curve Source #
(EllipticCurve curve, bool ~ BooleanOf curve) => Eq bool (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods (==) :: Point curve -> Point curve -> bool Source # (/=) :: Point curve -> Point curve -> bool Source #
(KnownNat n, EllipticCurve curve, Random (ScalarField curve), n <= PedersonSetupMaxSize) => PedersonSetup (Vector n :: Type -> Type) (Point curve :: Type) Source #
Instance details Defined in ZkFold.Base.Protocol.IVC.Commit Methods groupElements :: Vector n (Point curve) Source #
(EllipticCurve curve, Arbitrary (ScalarField curve)) => Arbitrary (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods arbitrary :: Gen (Point curve) # shrink :: Point curve -> [Point curve] #
Generic (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Associated Types type Rep (Point curve) :: Type -> Type # Methods from :: Point curve -> Rep (Point curve) x # to :: Rep (Point curve) x -> Point curve #
(EllipticCurve curve, Show (BaseField curve), Conditional (BooleanOf curve) String) => Show (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods showsPrec :: Int -> Point curve -> ShowS # show :: Point curve -> String # showList :: [Point curve] -> ShowS #
Binary (Point BLS12_381_G1) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods put :: Point BLS12_381_G1 -> Put # get :: Get (Point BLS12_381_G1) # putList :: [Point BLS12_381_G1] -> Put #
Binary (Point BLS12_381_G2) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods put :: Point BLS12_381_G2 -> Put # get :: Get (Point BLS12_381_G2) # putList :: [Point BLS12_381_G2] -> Put #
Binary (Point BN254_G1) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods put :: Point BN254_G1 -> Put # get :: Get (Point BN254_G1) # putList :: [Point BN254_G1] -> Put #
Binary (Point BN254_G2) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods put :: Point BN254_G2 -> Put # get :: Get (Point BN254_G2) # putList :: [Point BN254_G2] -> Put #
Binary (Point Pallas) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta Methods put :: Point Pallas -> Put # get :: Get (Point Pallas) # putList :: [Point Pallas] -> Put #
Binary (Point Vesta) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta Methods put :: Point Vesta -> Put # get :: Get (Point Vesta) # putList :: [Point Vesta] -> Put #
(EllipticCurve curve, BooleanOf curve ~ Bool) => Eq (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods (==) :: Point curve -> Point curve -> Bool # (/=) :: Point curve -> Point curve -> Bool #
(EllipticCurve curve, AdditiveGroup (BaseField curve)) => AdditiveGroup (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods (-) :: Point curve -> Point curve -> Point curve Source # negate :: Point curve -> Point curve Source #
EllipticCurve curve => AdditiveMonoid (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods zero :: Point curve Source #
EllipticCurve curve => AdditiveSemigroup (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods (+) :: Point curve -> Point curve -> Point curve Source #
(field ~ BaseField curve, BoolType (BooleanOf curve), AdditiveMonoid field) => ProjectivePlanar (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods pointInf :: Point curve Source #
(Symbolic ctx, SymbolicOutput bool, SymbolicOutput field, bool ~ BooleanOf curve, field ~ BaseField curve, Context bool ~ ctx, Context field ~ ctx) => SymbolicData (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Associated Types type Context (Point curve) :: (Type -> Type) -> Type Source # type Support (Point curve) Source # type Layout (Point curve) :: Type -> Type Source # type Payload (Point curve) :: Type -> Type Source # Methods arithmetize :: Point curve -> Support (Point curve) -> Context (Point curve) (Layout (Point curve)) Source # payload :: Point curve -> Support (Point curve) -> Payload (Point curve) (WitnessField (Context (Point curve))) Source # restore :: Context (Point curve) ~ c => (Support (Point curve) -> (c (Layout (Point curve)), Payload (Point curve) (WitnessField c))) -> Point curve Source #
(EllipticCurve c, SymbolicData (Point c), l ~ Layout (Point c), ctx ~ Context (Point c), Symbolic ctx, a ~ BaseField ctx, bits ~ NumberOfBits a, BooleanOf c ~ Bool ctx) => Scale (FieldElement ctx) (Point c) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Methods scale :: FieldElement ctx -> Point c -> Point c Source #
type Rep (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class type Rep (Point curve) = D1 ('MetaData "Point" "ZkFold.Base.Algebra.EllipticCurve.Class" "symbolic-base-0.1.0.0-inplace" 'False) (C1 ('MetaCons "Point" 'PrefixI 'True) (S1 ('MetaSel ('Just "_x") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BaseField curve)) :: (S1 ('MetaSel ('Just "_y") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BaseField curve)) :: S1 ('MetaSel ('Just "_isInf") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BooleanOf curve)))))
type Context (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class type Context (Point curve) = GContext (Rep (Point curve))
type Layout (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class type Layout (Point curve) = GLayout (Rep (Point curve))
type Payload (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class type Payload (Point curve) = GPayload (Rep (Point curve))
type Support (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class type Support (Point curve) = GSupport (Rep (Point curve))

class Planar field plane where Source #

Methods

pointXY :: field -> field -> plane Source #

Instances

Instances details

(field ~ BaseField curve, bool ~ BooleanOf curve, BoolType bool) => Planar field (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods pointXY :: field -> field -> Point curve Source #

class ProjectivePlanar plane where Source #

Methods

pointInf :: plane Source #

Instances

Instances details

(field ~ BaseField curve, BoolType (BooleanOf curve), AdditiveMonoid field) => ProjectivePlanar (CompressedPoint curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods pointInf :: CompressedPoint curve Source #
(field ~ BaseField curve, BoolType (BooleanOf curve), AdditiveMonoid field) => ProjectivePlanar (Point curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods pointInf :: Point curve Source #

class (BoolType (BooleanOf curve), AdditiveMonoid (BaseField curve), Conditional (BooleanOf curve) (BaseField curve), Conditional (BooleanOf curve) (BooleanOf curve), Eq (BooleanOf curve) (BaseField curve), Eq (BooleanOf curve) (BooleanOf curve)) => EllipticCurve curve where Source #

Associated Types

type BaseField curve :: Type Source #

type ScalarField curve :: Type Source #

type BooleanOf curve :: Type Source #

type BooleanOf curve = Bool

Methods

pointGen :: Point curve Source #

add :: Point curve -> Point curve -> Point curve Source #

mul :: ScalarField curve -> Point curve -> Point curve Source #

Instances

Instances details

EllipticCurve BLS12_381_G1 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Associated Types type BaseField BLS12_381_G1 Source # type ScalarField BLS12_381_G1 Source # type BooleanOf BLS12_381_G1 Source # Methods pointGen :: Point BLS12_381_G1 Source # add :: Point BLS12_381_G1 -> Point BLS12_381_G1 -> Point BLS12_381_G1 Source # mul :: ScalarField BLS12_381_G1 -> Point BLS12_381_G1 -> Point BLS12_381_G1 Source #
EllipticCurve BLS12_381_G2 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Associated Types type BaseField BLS12_381_G2 Source # type ScalarField BLS12_381_G2 Source # type BooleanOf BLS12_381_G2 Source # Methods pointGen :: Point BLS12_381_G2 Source # add :: Point BLS12_381_G2 -> Point BLS12_381_G2 -> Point BLS12_381_G2 Source # mul :: ScalarField BLS12_381_G2 -> Point BLS12_381_G2 -> Point BLS12_381_G2 Source #
EllipticCurve BN254_G1 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Associated Types type BaseField BN254_G1 Source # type ScalarField BN254_G1 Source # type BooleanOf BN254_G1 Source # Methods pointGen :: Point BN254_G1 Source # add :: Point BN254_G1 -> Point BN254_G1 -> Point BN254_G1 Source # mul :: ScalarField BN254_G1 -> Point BN254_G1 -> Point BN254_G1 Source #
EllipticCurve BN254_G2 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Associated Types type BaseField BN254_G2 Source # type ScalarField BN254_G2 Source # type BooleanOf BN254_G2 Source # Methods pointGen :: Point BN254_G2 Source # add :: Point BN254_G2 -> Point BN254_G2 -> Point BN254_G2 Source # mul :: ScalarField BN254_G2 -> Point BN254_G2 -> Point BN254_G2 Source #
EllipticCurve Ed25519 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 Source # type ScalarField Ed25519 Source # type BooleanOf Ed25519 Source # Methods pointGen :: Point Ed25519 Source # add :: Point Ed25519 -> Point Ed25519 -> Point Ed25519 Source # mul :: ScalarField Ed25519 -> Point Ed25519 -> Point Ed25519 Source #
EllipticCurve Pallas Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta Associated Types type BaseField Pallas Source # type ScalarField Pallas Source # type BooleanOf Pallas Source # Methods pointGen :: Point Pallas Source # add :: Point Pallas -> Point Pallas -> Point Pallas Source # mul :: ScalarField Pallas -> Point Pallas -> Point Pallas Source #
EllipticCurve Vesta Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta Associated Types type BaseField Vesta Source # type ScalarField Vesta Source # type BooleanOf Vesta Source # Methods pointGen :: Point Vesta Source # add :: Point Vesta -> Point Vesta -> Point Vesta Source # mul :: ScalarField Vesta -> Point Vesta -> Point Vesta Source #
EllipticCurve Secp256k1 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Secp256k1 Associated Types type BaseField Secp256k1 Source # type ScalarField Secp256k1 Source # type BooleanOf Secp256k1 Source # Methods pointGen :: Point Secp256k1 Source # add :: Point Secp256k1 -> Point Secp256k1 -> Point Secp256k1 Source # mul :: ScalarField Secp256k1 -> Point Secp256k1 -> Point Secp256k1 Source #
(Symbolic c, NFData (c (Vector Size))) => EllipticCurve (AcEd25519 c) Source #	Ed25519 with `UInt 256 ArithmeticCircuit a` as computational backend
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Associated Types type BaseField (AcEd25519 c) Source # type ScalarField (AcEd25519 c) Source # type BooleanOf (AcEd25519 c) Source # Methods pointGen :: Point (AcEd25519 c) Source # add :: Point (AcEd25519 c) -> Point (AcEd25519 c) -> Point (AcEd25519 c) Source # mul :: ScalarField (AcEd25519 c) -> Point (AcEd25519 c) -> Point (AcEd25519 c) Source #

class (EllipticCurve curve1, EllipticCurve curve2, ScalarField curve1 ~ ScalarField curve2, Eq (TargetGroup curve1 curve2), MultiplicativeGroup (TargetGroup curve1 curve2), Exponent (TargetGroup curve1 curve2) (ScalarField curve1)) => Pairing curve1 curve2 where Source #

Associated Types

type TargetGroup curve1 curve2 :: Type Source #

Methods

pairing :: Point curve1 -> Point curve2 -> TargetGroup curve1 curve2 Source #

Instances

Instances details

Pairing BLS12_381_G1 BLS12_381_G2 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Associated Types type TargetGroup BLS12_381_G1 BLS12_381_G2 Source # Methods pairing :: Point BLS12_381_G1 -> Point BLS12_381_G2 -> TargetGroup BLS12_381_G1 BLS12_381_G2 Source #
Pairing BN254_G1 BN254_G2 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Associated Types type TargetGroup BN254_G1 BN254_G2 Source # Methods pairing :: Point BN254_G1 -> Point BN254_G2 -> TargetGroup BN254_G1 BN254_G2 Source #

pointAdd :: EllipticCurve curve => Field (BaseField curve) => Point curve -> Point curve -> Point curve Source #

pointDouble :: EllipticCurve curve => Field (BaseField curve) => Point curve -> Point curve Source #

addPoints :: EllipticCurve curve => Field (BaseField curve) => Point curve -> Point curve -> Point curve Source #

pointNegate :: EllipticCurve curve => AdditiveGroup (BaseField curve) => Point curve -> Point curve Source #

pointMul :: forall curve s. EllipticCurve curve => BinaryExpansion s => Bits s ~ [s] => Eq s => s -> Point curve -> Point curve Source #

class EllipticCurve curve => WeierstrassCurve curve where Source #

Methods

weierstrassA :: BaseField curve Source #

weierstrassB :: BaseField curve Source #

Instances

Instances details

WeierstrassCurve BLS12_381_G1 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods weierstrassA :: BaseField BLS12_381_G1 Source # weierstrassB :: BaseField BLS12_381_G1 Source #
WeierstrassCurve BLS12_381_G2 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods weierstrassA :: BaseField BLS12_381_G2 Source # weierstrassB :: BaseField BLS12_381_G2 Source #
WeierstrassCurve BN254_G1 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods weierstrassA :: BaseField BN254_G1 Source # weierstrassB :: BaseField BN254_G1 Source #
WeierstrassCurve BN254_G2 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BN254 Methods weierstrassA :: BaseField BN254_G2 Source # weierstrassB :: BaseField BN254_G2 Source #
WeierstrassCurve Pallas Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta Methods weierstrassA :: BaseField Pallas Source # weierstrassB :: BaseField Pallas Source #
WeierstrassCurve Vesta Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta Methods weierstrassA :: BaseField Vesta Source # weierstrassB :: BaseField Vesta Source #
WeierstrassCurve Secp256k1 Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Secp256k1 Methods weierstrassA :: BaseField Secp256k1 Source # weierstrassB :: BaseField Secp256k1 Source #

data CompressedPoint curve Source #

Constructors

CompressedPoint
Fields _x :: BaseField curve _bigY :: BooleanOf curve _isInf :: BooleanOf curve

Instances

Instances details

(EllipticCurve curve, bool ~ BooleanOf curve) => Conditional bool (CompressedPoint curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods bool :: CompressedPoint curve -> CompressedPoint curve -> bool -> CompressedPoint curve Source #
(EllipticCurve curve, bool ~ BooleanOf curve) => Eq bool (CompressedPoint curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods (==) :: CompressedPoint curve -> CompressedPoint curve -> bool Source # (/=) :: CompressedPoint curve -> CompressedPoint curve -> bool Source #
(EllipticCurve curve, AdditiveGroup (BaseField curve), Ord (BooleanOf curve) (BaseField curve), Arbitrary (ScalarField curve)) => Arbitrary (CompressedPoint curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods arbitrary :: Gen (CompressedPoint curve) # shrink :: CompressedPoint curve -> [CompressedPoint curve] #
Generic (CompressedPoint curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Associated Types type Rep (CompressedPoint curve) :: Type -> Type # Methods from :: CompressedPoint curve -> Rep (CompressedPoint curve) x # to :: Rep (CompressedPoint curve) x -> CompressedPoint curve #
(Show (BaseField curve), Conditional (BooleanOf curve) String, Show (BooleanOf curve)) => Show (CompressedPoint curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods showsPrec :: Int -> CompressedPoint curve -> ShowS # show :: CompressedPoint curve -> String # showList :: [CompressedPoint curve] -> ShowS #
Binary (CompressedPoint BLS12_381_G1) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods put :: CompressedPoint BLS12_381_G1 -> Put # get :: Get (CompressedPoint BLS12_381_G1) # putList :: [CompressedPoint BLS12_381_G1] -> Put #
Binary (CompressedPoint BLS12_381_G2) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381 Methods put :: CompressedPoint BLS12_381_G2 -> Put # get :: Get (CompressedPoint BLS12_381_G2) # putList :: [CompressedPoint BLS12_381_G2] -> Put #
(EllipticCurve curve, BooleanOf curve ~ Bool) => Eq (CompressedPoint curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods (==) :: CompressedPoint curve -> CompressedPoint curve -> Bool # (/=) :: CompressedPoint curve -> CompressedPoint curve -> Bool #
(field ~ BaseField curve, BoolType (BooleanOf curve), AdditiveMonoid field) => ProjectivePlanar (CompressedPoint curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class Methods pointInf :: CompressedPoint curve Source #
type Rep (CompressedPoint curve) Source #
Instance details Defined in ZkFold.Base.Algebra.EllipticCurve.Class type Rep (CompressedPoint curve) = D1 ('MetaData "CompressedPoint" "ZkFold.Base.Algebra.EllipticCurve.Class" "symbolic-base-0.1.0.0-inplace" 'False) (C1 ('MetaCons "CompressedPoint" 'PrefixI 'True) (S1 ('MetaSel ('Just "_x") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BaseField curve)) :: (S1 ('MetaSel ('Just "_bigY") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BooleanOf curve)) :: S1 ('MetaSel ('Just "_isInf") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (BooleanOf curve)))))

pointCompressed :: BoolType (BooleanOf curve) => BaseField curve -> BooleanOf curve -> CompressedPoint curve Source #

compress :: (AdditiveGroup (BaseField curve), EllipticCurve curve, Ord (BooleanOf curve) (BaseField curve)) => Point curve -> CompressedPoint curve Source #

decompress :: forall curve. (WeierstrassCurve curve, FiniteField (BaseField curve), Ord (BooleanOf curve) (BaseField curve)) => CompressedPoint curve -> Point curve Source #