ZkFold.Base.Algebra.EllipticCurve.Class

Documentation

data Point (curve :: Type)

Constructors

Point

Fields

• _x :: BaseField curve
• _y :: BaseField curve
• _isInf :: BooleanOf curve

Instances

(EllipticCurve curve, Random (ScalarField curve)) => PedersonSetup List (Point curve :: Type)

Defined in ZkFold.Base.Protocol.IVC.Commit

Methods

groupElements :: [Point curve]

(PedersonSetup s (Point curve), Functor s) => PedersonSetup (s :: Type -> Type) (Constant (Point curve) a :: Type)

Defined in ZkFold.Base.Protocol.IVC.Commit

Methods

groupElements :: s (Constant (Point curve) a)

(EllipticCurve curve, AdditiveGroup (BaseField curve)) => Scale Integer (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

scale :: Integer -> Point curve -> Point curve

EllipticCurve curve => Scale Natural (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

scale :: Natural -> Point curve -> Point curve

(EllipticCurve curve, BooleanOf curve ~ Bool, Eq s, BinaryExpansion s, Bits s ~ [s]) => Scale s (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

scale :: s -> Point curve -> Point curve

(field ~ BaseField curve, bool ~ BooleanOf curve, BoolType bool) => Planar field (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

pointXY :: field -> field -> Point curve

(EllipticCurve curve, bool ~ BooleanOf curve) => Conditional bool (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

bool :: Point curve -> Point curve -> bool -> Point curve

(EllipticCurve curve, bool ~ BooleanOf curve) => Eq bool (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

(==) :: Point curve -> Point curve -> bool

(/=) :: Point curve -> Point curve -> bool

(KnownNat n, EllipticCurve curve, Random (ScalarField curve), n <= PedersonSetupMaxSize) => PedersonSetup (Vector n :: Type -> Type) (Point curve :: Type)

Defined in ZkFold.Base.Protocol.IVC.Commit

Methods

groupElements :: Vector n (Point curve)

(EllipticCurve curve, Arbitrary (ScalarField curve)) => Arbitrary (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

arbitrary :: Gen (Point curve)

shrink :: Point curve -> [Point curve]

Generic (Point curve)

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)

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)

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)

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)

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)

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)

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

Methods

put :: Point Pallas -> Put

get :: Get (Point Pallas)

putList :: [Point Pallas] -> Put

Binary (Point Vesta)

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)

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)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

(-) :: Point curve -> Point curve -> Point curve

negate :: Point curve -> Point curve

EllipticCurve curve => AdditiveMonoid (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

zero :: Point curve

EllipticCurve curve => AdditiveSemigroup (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

(+) :: Point curve -> Point curve -> Point curve

(field ~ BaseField curve, BoolType (BooleanOf curve), AdditiveMonoid field) => ProjectivePlanar (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

pointInf :: Point curve

(Symbolic ctx, SymbolicOutput bool, SymbolicOutput field, bool ~ BooleanOf curve, field ~ BaseField curve, Context bool ~ ctx, Context field ~ ctx) => SymbolicData (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Associated Types

type Context (Point curve) :: (Type -> Type) -> Type

type Support (Point curve)

type Layout (Point curve) :: Type -> Type

type Payload (Point curve) :: Type -> Type

Methods

arithmetize :: Point curve -> Support (Point curve) -> Context (Point curve) (Layout (Point curve))

payload :: Point curve -> Support (Point curve) -> Payload (Point curve) (WitnessField (Context (Point curve)))

restore :: Context (Point curve) ~ c => (Support (Point curve) -> (c (Layout (Point curve)), Payload (Point curve) (WitnessField c))) -> Point curve

(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)

Defined in ZkFold.Symbolic.Data.Ed25519

Methods

scale :: FieldElement ctx -> Point c -> Point c

type Rep (Point curve)

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)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

type Context (Point curve) = GContext (Rep (Point curve))

type Layout (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

type Layout (Point curve) = GLayout (Rep (Point curve))

type Payload (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

type Payload (Point curve) = GPayload (Rep (Point curve))

type Support (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

type Support (Point curve) = GSupport (Rep (Point curve))

class Planar field plane where

Methods

pointXY :: field -> field -> plane

Instances

(field ~ BaseField curve, bool ~ BooleanOf curve, BoolType bool) => Planar field (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

pointXY :: field -> field -> Point curve

class ProjectivePlanar plane where

Methods

pointInf :: plane

Instances

(field ~ BaseField curve, BoolType (BooleanOf curve), AdditiveMonoid field) => ProjectivePlanar (CompressedPoint curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

pointInf :: CompressedPoint curve

(field ~ BaseField curve, BoolType (BooleanOf curve), AdditiveMonoid field) => ProjectivePlanar (Point curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

pointInf :: Point curve

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

Associated Types

type BaseField curve :: Type

type ScalarField curve :: Type

type BooleanOf curve :: Type

type BooleanOf curve = Bool

Methods

pointGen :: Point curve

add :: Point curve -> Point curve -> Point curve

mul :: ScalarField curve -> Point curve -> Point curve

Instances

EllipticCurve BLS12_381_G1

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type BaseField BLS12_381_G1

type ScalarField BLS12_381_G1

type BooleanOf BLS12_381_G1

Methods

pointGen :: Point BLS12_381_G1

add :: Point BLS12_381_G1 -> Point BLS12_381_G1 -> Point BLS12_381_G1

mul :: ScalarField BLS12_381_G1 -> Point BLS12_381_G1 -> Point BLS12_381_G1

EllipticCurve BLS12_381_G2

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type BaseField BLS12_381_G2

type ScalarField BLS12_381_G2

type BooleanOf BLS12_381_G2

Methods

pointGen :: Point BLS12_381_G2

add :: Point BLS12_381_G2 -> Point BLS12_381_G2 -> Point BLS12_381_G2

mul :: ScalarField BLS12_381_G2 -> Point BLS12_381_G2 -> Point BLS12_381_G2

EllipticCurve BN254_G1

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Associated Types

type BaseField BN254_G1

type ScalarField BN254_G1

type BooleanOf BN254_G1

Methods

pointGen :: Point BN254_G1

add :: Point BN254_G1 -> Point BN254_G1 -> Point BN254_G1

mul :: ScalarField BN254_G1 -> Point BN254_G1 -> Point BN254_G1

EllipticCurve BN254_G2

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Associated Types

type BaseField BN254_G2

type ScalarField BN254_G2

type BooleanOf BN254_G2

Methods

pointGen :: Point BN254_G2

add :: Point BN254_G2 -> Point BN254_G2 -> Point BN254_G2

mul :: ScalarField BN254_G2 -> Point BN254_G2 -> Point BN254_G2

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

EllipticCurve Pallas

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

Associated Types

type BaseField Pallas

type ScalarField Pallas

type BooleanOf Pallas

Methods

pointGen :: Point Pallas

add :: Point Pallas -> Point Pallas -> Point Pallas

mul :: ScalarField Pallas -> Point Pallas -> Point Pallas

EllipticCurve Vesta

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

Associated Types

type BaseField Vesta

type ScalarField Vesta

type BooleanOf Vesta

Methods

pointGen :: Point Vesta

add :: Point Vesta -> Point Vesta -> Point Vesta

mul :: ScalarField Vesta -> Point Vesta -> Point Vesta

EllipticCurve Secp256k1

Defined in ZkFold.Base.Algebra.EllipticCurve.Secp256k1

Associated Types

type BaseField Secp256k1

type ScalarField Secp256k1

type BooleanOf Secp256k1

Methods

pointGen :: Point Secp256k1

add :: Point Secp256k1 -> Point Secp256k1 -> Point Secp256k1

mul :: ScalarField Secp256k1 -> Point Secp256k1 -> Point Secp256k1

(Symbolic c, NFData (c (Vector Size))) => EllipticCurve (AcEd25519 c)

Ed25519 with UInt 256 ArithmeticCircuit a as computational backend

Defined in ZkFold.Symbolic.Data.Ed25519

Associated Types

type BaseField (AcEd25519 c)

type ScalarField (AcEd25519 c)

type BooleanOf (AcEd25519 c)

Methods

pointGen :: Point (AcEd25519 c)

add :: Point (AcEd25519 c) -> Point (AcEd25519 c) -> Point (AcEd25519 c)

mul :: ScalarField (AcEd25519 c) -> Point (AcEd25519 c) -> Point (AcEd25519 c)

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

Associated Types

type TargetGroup curve1 curve2 :: Type

Methods

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

Instances

Pairing BLS12_381_G1 BLS12_381_G2

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type TargetGroup BLS12_381_G1 BLS12_381_G2

Methods

pairing :: Point BLS12_381_G1 -> Point BLS12_381_G2 -> TargetGroup BLS12_381_G1 BLS12_381_G2

Pairing BN254_G1 BN254_G2

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Associated Types

type TargetGroup BN254_G1 BN254_G2

Methods

pairing :: Point BN254_G1 -> Point BN254_G2 -> TargetGroup BN254_G1 BN254_G2

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

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

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

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

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

class EllipticCurve curve => WeierstrassCurve curve where

Methods

weierstrassA :: BaseField curve

weierstrassB :: BaseField curve

Instances

WeierstrassCurve BLS12_381_G1

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

weierstrassA :: BaseField BLS12_381_G1

weierstrassB :: BaseField BLS12_381_G1

WeierstrassCurve BLS12_381_G2

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

weierstrassA :: BaseField BLS12_381_G2

weierstrassB :: BaseField BLS12_381_G2

WeierstrassCurve BN254_G1

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

weierstrassA :: BaseField BN254_G1

weierstrassB :: BaseField BN254_G1

WeierstrassCurve BN254_G2

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

weierstrassA :: BaseField BN254_G2

weierstrassB :: BaseField BN254_G2

WeierstrassCurve Pallas

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

Methods

weierstrassA :: BaseField Pallas

weierstrassB :: BaseField Pallas

WeierstrassCurve Vesta

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

Methods

weierstrassA :: BaseField Vesta

weierstrassB :: BaseField Vesta

WeierstrassCurve Secp256k1

Defined in ZkFold.Base.Algebra.EllipticCurve.Secp256k1

Methods

weierstrassA :: BaseField Secp256k1

weierstrassB :: BaseField Secp256k1

data CompressedPoint curve

Constructors

CompressedPoint

Fields

• _x :: BaseField curve
• _bigY :: BooleanOf curve
• _isInf :: BooleanOf curve

Instances

(EllipticCurve curve, bool ~ BooleanOf curve) => Conditional bool (CompressedPoint curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

bool :: CompressedPoint curve -> CompressedPoint curve -> bool -> CompressedPoint curve

(EllipticCurve curve, bool ~ BooleanOf curve) => Eq bool (CompressedPoint curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

(==) :: CompressedPoint curve -> CompressedPoint curve -> bool

(/=) :: CompressedPoint curve -> CompressedPoint curve -> bool

(EllipticCurve curve, AdditiveGroup (BaseField curve), Ord (BooleanOf curve) (BaseField curve), Arbitrary (ScalarField curve)) => Arbitrary (CompressedPoint curve)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

arbitrary :: Gen (CompressedPoint curve)

shrink :: CompressedPoint curve -> [CompressedPoint curve]

Generic (CompressedPoint curve)

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)

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)

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)

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)

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)

Defined in ZkFold.Base.Algebra.EllipticCurve.Class

Methods

pointInf :: CompressedPoint curve

type Rep (CompressedPoint curve)

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

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

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