ZkFold.Symbolic.Data.FFA

Documentation

data FFA p r c

Constructors

FFA

Fields

• nativeResidue :: FieldElement c
• uintResidue :: UIntFFA p r c

Instances

(Symbolic c, KnownFFA p r c, FromConstant a (Zp p)) => FromConstant a (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

fromConstant :: a -> FFA p r c

(Symbolic c, KnownFFA p r c, Scale a (Zp p)) => Scale a (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

scale :: a -> FFA p r c -> FFA p r c

(Symbolic c, KnownFFA p r c, b ~ Bool c) => Conditional b (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

bool :: FFA p r c -> FFA p r c -> b -> FFA p r c

(Symbolic ctx, KnownFFA BLS12_381_Base 'Auto ctx) => CyclicGroup (BLS12_381_G1_Point ctx)

Defined in ZkFold.Symbolic.Data.BLS12_381

Associated Types

type ScalarFieldOf (BLS12_381_G1_Point ctx)

Methods

pointGen :: BLS12_381_G1_Point ctx

(Symbolic ctx, KnownFFA Ed25519_Base 'Auto ctx) => CyclicGroup (Ed25519_Point ctx)

Defined in ZkFold.Symbolic.Data.Ed25519

Associated Types

type ScalarFieldOf (Ed25519_Point ctx)

Methods

pointGen :: Ed25519_Point ctx

(Symbolic ctx, KnownFFA Secp256k1_Base 'Auto ctx) => CyclicGroup (Secp256k1_Point ctx)

Defined in ZkFold.Symbolic.Data.Secp256k1

Associated Types

type ScalarFieldOf (Secp256k1_Point ctx)

Methods

pointGen :: Secp256k1_Point ctx

(Symbolic ctx, a ~ BaseField ctx, bits ~ NumberOfBits a, KnownFFA BLS12_381_Base 'Auto ctx) => Scale (FieldElement ctx) (BLS12_381_G1_Point ctx)

Defined in ZkFold.Symbolic.Data.BLS12_381

Methods

scale :: FieldElement ctx -> BLS12_381_G1_Point ctx -> BLS12_381_G1_Point ctx

(Symbolic ctx, a ~ BaseField ctx, bits ~ NumberOfBits a, KnownFFA Ed25519_Base 'Auto ctx) => Scale (FieldElement ctx) (Ed25519_Point ctx)

Defined in ZkFold.Symbolic.Data.Ed25519

Methods

scale :: FieldElement ctx -> Ed25519_Point ctx -> Ed25519_Point ctx

(Symbolic ctx, a ~ BaseField ctx, bits ~ NumberOfBits a, KnownFFA Secp256k1_Base 'Auto ctx) => Scale (FieldElement ctx) (Secp256k1_Point ctx)

Defined in ZkFold.Symbolic.Data.Secp256k1

Methods

scale :: FieldElement ctx -> Secp256k1_Point ctx -> Secp256k1_Point ctx

Generic (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Associated Types

type Rep (FFA p r c) :: Type -> Type

Methods

from :: FFA p r c -> Rep (FFA p r c) x

to :: Rep (FFA p r c) x -> FFA p r c

(Show (FieldElement c), Show (UIntFFA p r c)) => Show (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

showsPrec :: Int -> FFA p r c -> ShowS

show :: FFA p r c -> String

showList :: [FFA p r c] -> ShowS

(NFData (FieldElement c), NFData (UIntFFA p r c)) => NFData (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

rnf :: FFA p r c -> ()

(Symbolic c, KnownFFA p r c) => AdditiveGroup (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

(-) :: FFA p r c -> FFA p r c -> FFA p r c

negate :: FFA p r c -> FFA p r c

(Symbolic c, KnownFFA p r c) => AdditiveMonoid (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

zero :: FFA p r c

(Symbolic c, KnownFFA p r c) => AdditiveSemigroup (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

(+) :: FFA p r c -> FFA p r c -> FFA p r c

(Symbolic c, KnownFFA p r c) => BinaryExpansion (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Associated Types

type Bits (FFA p r c)

Methods

binaryExpansion :: FFA p r c -> Bits (FFA p r c)

fromBinary :: Bits (FFA p r c) -> FFA p r c

(Symbolic c, KnownFFA p r c, Prime p) => Field (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

(//) :: FFA p r c -> FFA p r c -> FFA p r c

finv :: FFA p r c -> FFA p r c

rootOfUnity :: Natural -> Maybe (FFA p r c)

Finite (Zp p) => Finite (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Associated Types

type Order (FFA p r c) :: Natural

(Symbolic c, KnownFFA p r c) => MultiplicativeMonoid (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

one :: FFA p r c

(Symbolic c, KnownFFA p r c) => MultiplicativeSemigroup (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

(*) :: FFA p r c -> FFA p r c -> FFA p r c

(Symbolic c, KnownFFA p r c) => Ring (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

(Symbolic c, KnownFFA p r c) => Semiring (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

(Arithmetic a, KnownFFA p r (Interpreter a)) => ToConstant (FFA p r (Interpreter a))

Defined in ZkFold.Symbolic.Data.FFA

Associated Types

type Const (FFA p r (Interpreter a))

Methods

toConstant :: FFA p r (Interpreter a) -> Const (FFA p r (Interpreter a))

(Symbolic c, KnownFFA p r c) => SymbolicData (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Associated Types

type Context (FFA p r c) :: (Type -> Type) -> Type

type Support (FFA p r c)

type Layout (FFA p r c) :: Type -> Type

type Payload (FFA p r c) :: Type -> Type

Methods

arithmetize :: FFA p r c -> Support (FFA p r c) -> Context (FFA p r c) (Layout (FFA p r c))

payload :: FFA p r c -> Support (FFA p r c) -> Payload (FFA p r c) (WitnessField (Context (FFA p r c)))

restore :: Context (FFA p r c) ~ c0 => (Support (FFA p r c) -> (c0 (Layout (FFA p r c)), Payload (FFA p r c) (WitnessField c0))) -> FFA p r c

(Symbolic c, KnownFFA p r c) => Eq (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Associated Types

type BooleanOf (FFA p r c)

Methods

(==) :: FFA p r c -> FFA p r c -> BooleanOf (FFA p r c)

(/=) :: FFA p r c -> FFA p r c -> BooleanOf (FFA p r c)

(Symbolic c, KnownFFA p r c) => SymbolicInput (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

isValid :: FFA p r c -> Bool (Context (FFA p r c))

(Symbolic c, KnownFFA p r c, Prime p) => Exponent (FFA p r c) Integer

Defined in ZkFold.Symbolic.Data.FFA

Methods

(^) :: FFA p r c -> Integer -> FFA p r c

(Symbolic c, KnownFFA p r c) => Exponent (FFA p r c) Natural

Defined in ZkFold.Symbolic.Data.FFA

Methods

(^) :: FFA p r c -> Natural -> FFA p r c

FromConstant (FFA p r c) (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

fromConstant :: FFA p r c -> FFA p r c

(Symbolic c, KnownFFA p r c) => Scale (FFA p r c) (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

Methods

scale :: FFA p r c -> FFA p r c -> FFA p r c

type ScalarFieldOf (BLS12_381_G1_Point ctx)

Defined in ZkFold.Symbolic.Data.BLS12_381

type ScalarFieldOf (BLS12_381_G1_Point ctx) = FieldElement ctx

type ScalarFieldOf (Ed25519_Point ctx)

Defined in ZkFold.Symbolic.Data.Ed25519

type ScalarFieldOf (Ed25519_Point ctx) = FieldElement ctx

type ScalarFieldOf (Secp256k1_Point ctx)

Defined in ZkFold.Symbolic.Data.Secp256k1

type ScalarFieldOf (Secp256k1_Point ctx) = FieldElement ctx

type Rep (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

type Rep (FFA p r c)

type Bits (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

type Bits (FFA p r c) = ByteString (NumberOfBits (Zp p)) c

type Const (FFA p r (Interpreter a))

Defined in ZkFold.Symbolic.Data.FFA

type Const (FFA p r (Interpreter a)) = Zp p

type Order (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

type Order (FFA p r c) = p

type Context (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

type Context (FFA p r c) = GContext (Rep (FFA p r c))

type Layout (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

type Layout (FFA p r c) = GLayout (Rep (FFA p r c))

type Payload (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

type Payload (FFA p r c) = GPayload (Rep (FFA p r c))

type Support (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

type Support (FFA p r c) = GSupport (Rep (FFA p r c))

type BooleanOf (FFA p r c)

Defined in ZkFold.Symbolic.Data.FFA

type BooleanOf (FFA p r c) = GBooleanOf (Rep (FFA p r c))

type KnownFFA p r c = (KnownNat (FFAUIntSize p (Order (BaseField c))), KnownNat p, KnownRegisterSize r, KnownRegisters c (FFAUIntSize p (Order (BaseField c))) r, KnownNat (FFAMaxBits p c), KnownNat (GetRegisterSize (BaseField c) (FFAMaxBits p c) r), KnownRegisters c (FFAMaxBits p c) r, KnownNat (Ceil (GetRegisterSize (BaseField c) (FFAMaxBits p c) r) OrdWord), KnownRegisters c (NumberOfBits (Zp p)) r, KnownNat (GetRegisterSize (BaseField c) (NumberOfBits (Zp p)) r), KnownNat (NumberOfBits (Zp p)))