ZkFold.Base.Algebra.Basic.Field

Documentation

class IrreduciblePoly f (e :: Symbol) | e -> f where

Methods

irreduciblePoly :: Poly f

Instances

IrreduciblePoly Fq IP1

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

irreduciblePoly :: Poly Fq

IrreduciblePoly Fq2 IP2

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

irreduciblePoly :: Poly Fq2

IrreduciblePoly Fq6 IP3

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

irreduciblePoly :: Poly Fq6

IrreduciblePoly Fp "IP1"

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

irreduciblePoly :: Poly Fp

IrreduciblePoly Fp2 "IP2"

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

irreduciblePoly :: Poly Fp2

IrreduciblePoly Fp6 "IP3"

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

irreduciblePoly :: Poly Fp6

IrreduciblePoly (Zp PlutoEris_p) "i*sqrt5"

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

Methods

irreduciblePoly :: Poly (Zp PlutoEris_p)

data Zp (p :: Natural)

Instances

Binary BLS12_381_G1_CompressedPoint

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

put :: BLS12_381_G1_CompressedPoint -> Put

get :: Get BLS12_381_G1_CompressedPoint

putList :: [BLS12_381_G1_CompressedPoint] -> Put

Binary BLS12_381_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

put :: BLS12_381_G1_Point -> Put

get :: Get BLS12_381_G1_Point

putList :: [BLS12_381_G1_Point] -> Put

Binary BLS12_381_G2_CompressedPoint

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

put :: BLS12_381_G2_CompressedPoint -> Put

get :: Get BLS12_381_G2_CompressedPoint

putList :: [BLS12_381_G2_CompressedPoint] -> Put

Binary BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

put :: BLS12_381_G2_Point -> Put

get :: Get BLS12_381_G2_Point

putList :: [BLS12_381_G2_Point] -> Put

Binary BN254_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

put :: BN254_G1_Point -> Put

get :: Get BN254_G1_Point

putList :: [BN254_G1_Point] -> Put

Binary BN254_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

put :: BN254_G2_Point -> Put

get :: Get BN254_G2_Point

putList :: [BN254_G2_Point] -> Put

Compressible BLS12_381_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type Compressed BLS12_381_G1_Point

Methods

pointCompressed :: BaseFieldOf BLS12_381_G1_Point -> BooleanOf (BaseFieldOf BLS12_381_G1_Point) -> Compressed BLS12_381_G1_Point

compress :: BLS12_381_G1_Point -> Compressed BLS12_381_G1_Point

decompress :: Compressed BLS12_381_G1_Point -> BLS12_381_G1_Point

Compressible BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type Compressed BLS12_381_G2_Point

Methods

pointCompressed :: BaseFieldOf BLS12_381_G2_Point -> BooleanOf (BaseFieldOf BLS12_381_G2_Point) -> Compressed BLS12_381_G2_Point

compress :: BLS12_381_G2_Point -> Compressed BLS12_381_G2_Point

decompress :: Compressed BLS12_381_G2_Point -> BLS12_381_G2_Point

CyclicGroup BLS12_381_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type ScalarFieldOf BLS12_381_G1_Point

Methods

pointGen :: BLS12_381_G1_Point

CyclicGroup BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type ScalarFieldOf BLS12_381_G2_Point

Methods

pointGen :: BLS12_381_G2_Point

CyclicGroup BN254_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Associated Types

type ScalarFieldOf BN254_G1_Point

Methods

pointGen :: BN254_G1_Point

CyclicGroup BN254_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Associated Types

type ScalarFieldOf BN254_G2_Point

Methods

pointGen :: BN254_G2_Point

CyclicGroup Ed25519_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519

Associated Types

type ScalarFieldOf Ed25519_Point

Methods

pointGen :: Ed25519_Point

CyclicGroup Pallas_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

Associated Types

type ScalarFieldOf Pallas_Point

Methods

pointGen :: Pallas_Point

CyclicGroup Vesta_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

Associated Types

type ScalarFieldOf Vesta_Point

Methods

pointGen :: Vesta_Point

CyclicGroup Eris_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

Associated Types

type ScalarFieldOf Eris_Point

Methods

pointGen :: Eris_Point

CyclicGroup Pluto_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

Associated Types

type ScalarFieldOf Pluto_Point

Methods

pointGen :: Pluto_Point

CyclicGroup Secp256k1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Secp256k1

Associated Types

type ScalarFieldOf Secp256k1_Point

Methods

pointGen :: Secp256k1_Point

Scale Fr BLS12_381_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

scale :: Fr -> BLS12_381_G1_Point -> BLS12_381_G1_Point

Scale Fr BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

scale :: Fr -> BLS12_381_G2_Point -> BLS12_381_G2_Point

Scale Fr BN254_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

scale :: Fr -> BN254_G1_Point -> BN254_G1_Point

Scale Fr BN254_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

scale :: Fr -> BN254_G2_Point -> BN254_G2_Point

Scale Fl Ed25519_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519

Methods

scale :: Fl -> Ed25519_Point -> Ed25519_Point

Scale Fp Vesta_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

Methods

scale :: Fp -> Vesta_Point -> Vesta_Point

Scale Fq Pallas_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

Methods

scale :: Fq -> Pallas_Point -> Pallas_Point

Scale Fn Secp256k1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Secp256k1

Methods

scale :: Fn -> Secp256k1_Point -> Secp256k1_Point

IrreduciblePoly Fq IP1

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

irreduciblePoly :: Poly Fq

IrreduciblePoly Fq2 IP2

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

irreduciblePoly :: Poly Fq2

IrreduciblePoly Fq6 IP3

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

irreduciblePoly :: Poly Fq6

IrreduciblePoly Fp "IP1"

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

irreduciblePoly :: Poly Fp

IrreduciblePoly Fp2 "IP2"

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

irreduciblePoly :: Poly Fp2

IrreduciblePoly Fp6 "IP3"

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

irreduciblePoly :: Poly Fp6

WeierstrassCurve "BLS12-381-G2" Fq2

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

weierstrassB :: Fq2

WeierstrassCurve "BN254_G2" Fp2

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

weierstrassB :: Fp2

Pairing BLS12_381_G1_Point BLS12_381_G2_Point BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

pairing :: BLS12_381_G1_Point -> BLS12_381_G2_Point -> BLS12_381_GT

Pairing BN254_G1_Point BN254_G2_Point BN254_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

pairing :: BN254_G1_Point -> BN254_G2_Point -> BN254_GT

(MultiplicativeGroup a, Order a ~ p) => Exponent a (Zp p)

Exponentiation by an element of a finite field is well-defined (and lawful) if and only if the base is a finite multiplicative group of a matching order.

Note that left distributivity is satisfied, meaning a ^ (m + n) = (a ^ m) * (a ^ n).

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(^) :: a -> Zp p -> a

KnownNat p => FromConstant Integer (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

fromConstant :: Integer -> Zp p

KnownNat p => FromConstant Natural (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

fromConstant :: Natural -> Zp p

KnownNat p => Scale Integer (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

scale :: Integer -> Zp p -> Zp p

KnownNat p => Scale Natural (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

scale :: Natural -> Zp p -> Zp p

Conditional Bool (Zp n)

Defined in ZkFold.Symbolic.Data.Conditional

Methods

bool :: Zp n -> Zp n -> Bool -> Zp n

WeierstrassCurve "Triton" (Ext2 (Zp PlutoEris_p) "i*sqrt5")

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

Methods

weierstrassB :: Ext2 (Zp PlutoEris_p) "i*sqrt5"

KnownNat p => Arbitrary (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

arbitrary :: Gen (Zp p)

shrink :: Zp p -> [Zp p]

FromJSON (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

parseJSON :: Value -> Parser (Zp p)

parseJSONList :: Value -> Parser [Zp p]

FromJSON (PlonkupProverSecret BLS12_381_G1_Point)

Defined in ZkFold.Base.Protocol.Plonkup.Prover.Secret

Methods

parseJSON :: Value -> Parser (PlonkupProverSecret BLS12_381_G1_Point)

parseJSONList :: Value -> Parser [PlonkupProverSecret BLS12_381_G1_Point]

ToJSON (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

toJSON :: Zp p -> Value

toEncoding :: Zp p -> Encoding

toJSONList :: [Zp p] -> Value

toEncodingList :: [Zp p] -> Encoding

ToJSON (PlonkupProverSecret BLS12_381_G1_Point)

Defined in ZkFold.Base.Protocol.Plonkup.Prover.Secret

Methods

toJSON :: PlonkupProverSecret BLS12_381_G1_Point -> Value

toEncoding :: PlonkupProverSecret BLS12_381_G1_Point -> Encoding

toJSONList :: [PlonkupProverSecret BLS12_381_G1_Point] -> Value

toEncodingList :: [PlonkupProverSecret BLS12_381_G1_Point] -> Encoding

Generic (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Associated Types

type Rep (Zp p) :: Type -> Type

Methods

from :: Zp p -> Rep (Zp p) x

to :: Rep (Zp p) x -> Zp p

KnownNat p => Num (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(+) :: Zp p -> Zp p -> Zp p

(-) :: Zp p -> Zp p -> Zp p

(*) :: Zp p -> Zp p -> Zp p

negate :: Zp p -> Zp p

abs :: Zp p -> Zp p

signum :: Zp p -> Zp p

fromInteger :: Integer -> Zp p

Prime p => Fractional (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(/) :: Zp p -> Zp p -> Zp p

recip :: Zp p -> Zp p

fromRational :: Rational -> Zp p

Show (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

showsPrec :: Int -> Zp p -> ShowS

show :: Zp p -> String

showList :: [Zp p] -> ShowS

KnownNat p => Binary (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

put :: Zp p -> Put

get :: Get (Zp p)

putList :: [Zp p] -> Put

NFData (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

rnf :: Zp p -> ()

KnownNat p => Eq (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(==) :: Zp p -> Zp p -> Bool

(/=) :: Zp p -> Zp p -> Bool

KnownNat p => Ord (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

compare :: Zp p -> Zp p -> Ordering

(<) :: Zp p -> Zp p -> Bool

(<=) :: Zp p -> Zp p -> Bool

(>) :: Zp p -> Zp p -> Bool

(>=) :: Zp p -> Zp p -> Bool

max :: Zp p -> Zp p -> Zp p

min :: Zp p -> Zp p -> Zp p

KnownNat p => Random (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

randomR :: RandomGen g => (Zp p, Zp p) -> g -> (Zp p, g)

random :: RandomGen g => g -> (Zp p, g)

randomRs :: RandomGen g => (Zp p, Zp p) -> g -> [Zp p]

randoms :: RandomGen g => g -> [Zp p]

KnownNat p => AdditiveGroup (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(-) :: Zp p -> Zp p -> Zp p

negate :: Zp p -> Zp p

KnownNat p => AdditiveMonoid (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

zero :: Zp p

KnownNat p => AdditiveSemigroup (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(+) :: Zp p -> Zp p -> Zp p

Prime p => BinaryExpansion (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Associated Types

type Bits (Zp p)

Methods

binaryExpansion :: Zp p -> Bits (Zp p)

fromBinary :: Bits (Zp p) -> Zp p

Prime p => DiscreteField' (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

equal :: Zp p -> Zp p -> Zp p

Prime p => Field (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(//) :: Zp p -> Zp p -> Zp p

finv :: Zp p -> Zp p

rootOfUnity :: Natural -> Maybe (Zp p)

(KnownNat p, KnownNat (NumberOfBits (Zp p))) => Finite (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Associated Types

type Order (Zp p) :: Natural

KnownNat p => MultiplicativeMonoid (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

one :: Zp p

KnownNat p => MultiplicativeSemigroup (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(*) :: Zp p -> Zp p -> Zp p

KnownNat p => Ring (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

KnownNat p => SemiEuclidean (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

divMod :: Zp p -> Zp p -> (Zp p, Zp p)

div :: Zp p -> Zp p -> Zp p

mod :: Zp p -> Zp p -> Zp p

KnownNat p => Semiring (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

ToConstant (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Associated Types

type Const (Zp p)

Methods

toConstant :: Zp p -> Const (Zp p)

Prime p => TrichotomyField (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

trichotomy :: Zp p -> Zp p -> Zp p

KnownNat n => Eq (Zp n)

Defined in ZkFold.Symbolic.Data.Eq

Associated Types

type BooleanOf (Zp n)

Methods

(==) :: Zp n -> Zp n -> BooleanOf (Zp n)

(/=) :: Zp n -> Zp n -> BooleanOf (Zp n)

KnownNat n => Ord (Zp n)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type OrderingOf (Zp n)

Methods

ordering :: Zp n -> Zp n -> Zp n -> OrderingOf (Zp n) -> Zp n

compare :: Zp n -> Zp n -> OrderingOf (Zp n)

(<) :: Zp n -> Zp n -> BooleanOf (Zp n)

(<=) :: Zp n -> Zp n -> BooleanOf (Zp n)

(>) :: Zp n -> Zp n -> BooleanOf (Zp n)

(>=) :: Zp n -> Zp n -> BooleanOf (Zp n)

max :: Zp n -> Zp n -> Zp n

min :: Zp n -> Zp n -> Zp n

PrimeField (Zp p) => ResidueField (Zp p)

Defined in ZkFold.Symbolic.MonadCircuit

Associated Types

type IntegralOf (Zp p)

Methods

fromIntegral :: IntegralOf (Zp p) -> Zp p

toIntegral :: Zp p -> IntegralOf (Zp p)

Prime p => Exponent (Zp p) Integer

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(^) :: Zp p -> Integer -> Zp p

KnownNat p => Exponent (Zp p) Natural

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(^) :: Zp p -> Natural -> Zp p

Scale (Zp PlutoEris_p) Eris_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

Methods

scale :: Zp PlutoEris_p -> Eris_Point -> Eris_Point

Scale (Zp PlutoEris_q) Pluto_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

Methods

scale :: Zp PlutoEris_q -> Pluto_Point -> Pluto_Point

IrreduciblePoly (Zp PlutoEris_p) "i*sqrt5"

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

Methods

irreduciblePoly :: Poly (Zp PlutoEris_p)

(Symbolic c, KnownNat n, KnownRegisterSize r) => StrictConv (Zp p) (UInt n r c)

Defined in ZkFold.Symbolic.Data.UInt

Methods

strictConv :: Zp p -> UInt n r c

Substitution (Vector n b) (Zp n) b

Defined in ZkFold.Base.Algebra.Polynomials.Multivariate.Substitution

Methods

subs :: Vector n b -> Zp n -> b

(Symbolic (Interpreter (Zp p)), KnownNat n, KnownRegisterSize r) => ToJSON (UInt n r (Interpreter (Zp p)))

Defined in ZkFold.Symbolic.Data.UInt

Methods

toJSON :: UInt n r (Interpreter (Zp p)) -> Value

toEncoding :: UInt n r (Interpreter (Zp p)) -> Encoding

toJSONList :: [UInt n r (Interpreter (Zp p))] -> Value

toEncodingList :: [UInt n r (Interpreter (Zp p))] -> Encoding

type Compressed BLS12_381_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

type Compressed BLS12_381_G1_Point = BLS12_381_G1_CompressedPoint

type Compressed BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

type Compressed BLS12_381_G2_Point = BLS12_381_G2_CompressedPoint

type ScalarFieldOf BLS12_381_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

type ScalarFieldOf BLS12_381_G1_Point = Fr

type ScalarFieldOf BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

type ScalarFieldOf BLS12_381_G2_Point = Fr

type ScalarFieldOf BN254_G1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

type ScalarFieldOf BN254_G1_Point = Fr

type ScalarFieldOf BN254_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

type ScalarFieldOf BN254_G2_Point = Fr

type ScalarFieldOf Ed25519_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Ed25519

type ScalarFieldOf Ed25519_Point = Fl

type ScalarFieldOf Pallas_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

type ScalarFieldOf Pallas_Point = Fq

type ScalarFieldOf Vesta_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Pasta

type ScalarFieldOf Vesta_Point = Fp

type ScalarFieldOf Eris_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

type ScalarFieldOf Eris_Point = Zp PlutoEris_p

type ScalarFieldOf Pluto_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

type ScalarFieldOf Pluto_Point = Zp PlutoEris_q

type ScalarFieldOf Secp256k1_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.Secp256k1

type ScalarFieldOf Secp256k1_Point = Fn

type Rep (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

type Rep (Zp p) = D1 ('MetaData "Zp" "ZkFold.Base.Algebra.Basic.Field" "symbolic-base-0.1.0.0-inplace" 'True) (C1 ('MetaCons "Zp" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Integer)))

type Bits (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

type Bits (Zp p) = [Zp p]

type Const (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

type Const (Zp p) = Natural

type Order (Zp p)

Defined in ZkFold.Base.Algebra.Basic.Field

type Order (Zp p) = p

type BooleanOf (Zp n)

Defined in ZkFold.Symbolic.Data.Eq

type BooleanOf (Zp n) = Bool

type OrderingOf (Zp n)

Defined in ZkFold.Symbolic.Data.Ord

type OrderingOf (Zp n) = Ordering

type IntegralOf (Zp p)

Defined in ZkFold.Symbolic.MonadCircuit

type IntegralOf (Zp p) = Integer

toZp :: forall p. KnownNat p => Integer -> Zp p

fromZp :: Zp p -> Natural

inv :: Integer -> Natural -> Natural

data Ext2 f (e :: Symbol)

Constructors

Ext2 f f

Instances

Binary BLS12_381_G2_CompressedPoint

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

put :: BLS12_381_G2_CompressedPoint -> Put

get :: Get BLS12_381_G2_CompressedPoint

putList :: [BLS12_381_G2_CompressedPoint] -> Put

Binary BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

put :: BLS12_381_G2_Point -> Put

get :: Get BLS12_381_G2_Point

putList :: [BLS12_381_G2_Point] -> Put

Binary BN254_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

put :: BN254_G2_Point -> Put

get :: Get BN254_G2_Point

putList :: [BN254_G2_Point] -> Put

Compressible BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type Compressed BLS12_381_G2_Point

Methods

pointCompressed :: BaseFieldOf BLS12_381_G2_Point -> BooleanOf (BaseFieldOf BLS12_381_G2_Point) -> Compressed BLS12_381_G2_Point

compress :: BLS12_381_G2_Point -> Compressed BLS12_381_G2_Point

decompress :: Compressed BLS12_381_G2_Point -> BLS12_381_G2_Point

CyclicGroup BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Associated Types

type ScalarFieldOf BLS12_381_G2_Point

Methods

pointGen :: BLS12_381_G2_Point

CyclicGroup BN254_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Associated Types

type ScalarFieldOf BN254_G2_Point

Methods

pointGen :: BN254_G2_Point

Scale Fr BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

scale :: Fr -> BLS12_381_G2_Point -> BLS12_381_G2_Point

Scale Fr BN254_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

scale :: Fr -> BN254_G2_Point -> BN254_G2_Point

IrreduciblePoly Fq2 IP2

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

irreduciblePoly :: Poly Fq2

IrreduciblePoly Fq6 IP3

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

irreduciblePoly :: Poly Fq6

IrreduciblePoly Fp2 "IP2"

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

irreduciblePoly :: Poly Fp2

IrreduciblePoly Fp6 "IP3"

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

irreduciblePoly :: Poly Fp6

WeierstrassCurve "BLS12-381-G2" Fq2

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

weierstrassB :: Fq2

WeierstrassCurve "BN254_G2" Fp2

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

weierstrassB :: Fp2

Pairing BLS12_381_G1_Point BLS12_381_G2_Point BLS12_381_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

pairing :: BLS12_381_G1_Point -> BLS12_381_G2_Point -> BLS12_381_GT

Pairing BN254_G1_Point BN254_G2_Point BN254_GT

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

pairing :: BN254_G1_Point -> BN254_G2_Point -> BN254_GT

(FromConstant f f', Field f') => FromConstant f (Ext2 f' e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

fromConstant :: f -> Ext2 f' e

Scale c f => Scale c (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

scale :: c -> Ext2 f e -> Ext2 f e

WeierstrassCurve "Triton" (Ext2 (Zp PlutoEris_p) "i*sqrt5")

Defined in ZkFold.Base.Algebra.EllipticCurve.PlutoEris

Methods

weierstrassB :: Ext2 (Zp PlutoEris_p) "i*sqrt5"

Conditional bool field => Conditional bool (Ext2 field i)

Defined in ZkFold.Symbolic.Data.Conditional

Methods

bool :: Ext2 field i -> Ext2 field i -> bool -> Ext2 field i

(Field f, Eq f, IrreduciblePoly f e) => FromConstant (Poly f) (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

fromConstant :: Poly f -> Ext2 f e

(Field f, Eq f, IrreduciblePoly f e, Arbitrary f) => Arbitrary (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

arbitrary :: Gen (Ext2 f e)

shrink :: Ext2 f e -> [Ext2 f e]

Generic (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Associated Types

type Rep (Ext2 f e) :: Type -> Type

Methods

from :: Ext2 f e -> Rep (Ext2 f e) x

to :: Rep (Ext2 f e) x -> Ext2 f e

Show f => Show (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

showsPrec :: Int -> Ext2 f e -> ShowS

show :: Ext2 f e -> String

showList :: [Ext2 f e] -> ShowS

Binary f => Binary (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

put :: Ext2 f e -> Put

get :: Get (Ext2 f e)

putList :: [Ext2 f e] -> Put

Eq f => Eq (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(==) :: Ext2 f e -> Ext2 f e -> Bool

(/=) :: Ext2 f e -> Ext2 f e -> Bool

Ord f => Ord (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

compare :: Ext2 f e -> Ext2 f e -> Ordering

(<) :: Ext2 f e -> Ext2 f e -> Bool

(<=) :: Ext2 f e -> Ext2 f e -> Bool

(>) :: Ext2 f e -> Ext2 f e -> Bool

(>=) :: Ext2 f e -> Ext2 f e -> Bool

max :: Ext2 f e -> Ext2 f e -> Ext2 f e

min :: Ext2 f e -> Ext2 f e -> Ext2 f e

Field f => AdditiveGroup (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(-) :: Ext2 f e -> Ext2 f e -> Ext2 f e

negate :: Ext2 f e -> Ext2 f e

Field f => AdditiveMonoid (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

zero :: Ext2 f e

Field f => AdditiveSemigroup (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(+) :: Ext2 f e -> Ext2 f e -> Ext2 f e

(Field f, Eq f, IrreduciblePoly f e) => Field (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(//) :: Ext2 f e -> Ext2 f e -> Ext2 f e

finv :: Ext2 f e -> Ext2 f e

rootOfUnity :: Natural -> Maybe (Ext2 f e)

(KnownNat (Order (Ext2 f e)), KnownNat (NumberOfBits (Ext2 f e))) => Finite (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Associated Types

type Order (Ext2 f e) :: Natural

(Field f, Eq f, IrreduciblePoly f e) => MultiplicativeMonoid (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

one :: Ext2 f e

(Field f, Eq f, IrreduciblePoly f e) => MultiplicativeSemigroup (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(*) :: Ext2 f e -> Ext2 f e -> Ext2 f e

(Field f, Eq f, IrreduciblePoly f e) => Ring (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

(Field f, Eq f, IrreduciblePoly f e) => Semiring (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Eq field => Eq (Ext2 field i)

Defined in ZkFold.Symbolic.Data.Eq

Associated Types

type BooleanOf (Ext2 field i)

Methods

(==) :: Ext2 field i -> Ext2 field i -> BooleanOf (Ext2 field i)

(/=) :: Ext2 field i -> Ext2 field i -> BooleanOf (Ext2 field i)

Field (Ext2 f e) => Exponent (Ext2 f e) Integer

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(^) :: Ext2 f e -> Integer -> Ext2 f e

MultiplicativeMonoid (Ext2 f e) => Exponent (Ext2 f e) Natural

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(^) :: Ext2 f e -> Natural -> Ext2 f e

FromConstant (Ext2 f e) (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

fromConstant :: Ext2 f e -> Ext2 f e

(Field f, Eq f, IrreduciblePoly f e) => Scale (Ext2 f e) (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

scale :: Ext2 f e -> Ext2 f e -> Ext2 f e

type Compressed BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

type Compressed BLS12_381_G2_Point = BLS12_381_G2_CompressedPoint

type ScalarFieldOf BLS12_381_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

type ScalarFieldOf BLS12_381_G2_Point = Fr

type ScalarFieldOf BN254_G2_Point

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

type ScalarFieldOf BN254_G2_Point = Fr

type Rep (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

type Rep (Ext2 f e) = D1 ('MetaData "Ext2" "ZkFold.Base.Algebra.Basic.Field" "symbolic-base-0.1.0.0-inplace" 'False) (C1 ('MetaCons "Ext2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 f) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 f)))

type Order (Ext2 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

type Order (Ext2 f e) = Order f ^ 2

type BooleanOf (Ext2 field i)

Defined in ZkFold.Symbolic.Data.Eq

type BooleanOf (Ext2 field i) = GBooleanOf (Rep (Ext2 field i))

data Ext3 f (e :: Symbol)

Constructors

Ext3 f f f

Instances

IrreduciblePoly Fq6 IP3

Defined in ZkFold.Base.Algebra.EllipticCurve.BLS12_381

Methods

irreduciblePoly :: Poly Fq6

IrreduciblePoly Fp6 "IP3"

Defined in ZkFold.Base.Algebra.EllipticCurve.BN254

Methods

irreduciblePoly :: Poly Fp6

(FromConstant f f', Field f') => FromConstant f (Ext3 f' ip)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

fromConstant :: f -> Ext3 f' ip

Scale c f => Scale c (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

scale :: c -> Ext3 f e -> Ext3 f e

Conditional bool field => Conditional bool (Ext3 field i)

Defined in ZkFold.Symbolic.Data.Conditional

Methods

bool :: Ext3 field i -> Ext3 field i -> bool -> Ext3 field i

(Field f, Eq f, IrreduciblePoly f e) => FromConstant (Poly f) (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

fromConstant :: Poly f -> Ext3 f e

(Field f, Eq f, IrreduciblePoly f e, Arbitrary f) => Arbitrary (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

arbitrary :: Gen (Ext3 f e)

shrink :: Ext3 f e -> [Ext3 f e]

Generic (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Associated Types

type Rep (Ext3 f e) :: Type -> Type

Methods

from :: Ext3 f e -> Rep (Ext3 f e) x

to :: Rep (Ext3 f e) x -> Ext3 f e

Show f => Show (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

showsPrec :: Int -> Ext3 f e -> ShowS

show :: Ext3 f e -> String

showList :: [Ext3 f e] -> ShowS

Binary f => Binary (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

put :: Ext3 f e -> Put

get :: Get (Ext3 f e)

putList :: [Ext3 f e] -> Put

Eq f => Eq (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(==) :: Ext3 f e -> Ext3 f e -> Bool

(/=) :: Ext3 f e -> Ext3 f e -> Bool

Ord f => Ord (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

compare :: Ext3 f e -> Ext3 f e -> Ordering

(<) :: Ext3 f e -> Ext3 f e -> Bool

(<=) :: Ext3 f e -> Ext3 f e -> Bool

(>) :: Ext3 f e -> Ext3 f e -> Bool

(>=) :: Ext3 f e -> Ext3 f e -> Bool

max :: Ext3 f e -> Ext3 f e -> Ext3 f e

min :: Ext3 f e -> Ext3 f e -> Ext3 f e

Field f => AdditiveGroup (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(-) :: Ext3 f e -> Ext3 f e -> Ext3 f e

negate :: Ext3 f e -> Ext3 f e

Field f => AdditiveMonoid (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

zero :: Ext3 f e

Field f => AdditiveSemigroup (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(+) :: Ext3 f e -> Ext3 f e -> Ext3 f e

(Field f, Eq f, IrreduciblePoly f e) => Field (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(//) :: Ext3 f e -> Ext3 f e -> Ext3 f e

finv :: Ext3 f e -> Ext3 f e

rootOfUnity :: Natural -> Maybe (Ext3 f e)

(KnownNat (Order (Ext3 f e)), KnownNat (NumberOfBits (Ext3 f e))) => Finite (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Associated Types

type Order (Ext3 f e) :: Natural

(Field f, Eq f, IrreduciblePoly f e) => MultiplicativeMonoid (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

one :: Ext3 f e

(Field f, Eq f, IrreduciblePoly f e) => MultiplicativeSemigroup (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(*) :: Ext3 f e -> Ext3 f e -> Ext3 f e

(Field f, Eq f, IrreduciblePoly f e) => Ring (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

(Field f, Eq f, IrreduciblePoly f e) => Semiring (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Eq field => Eq (Ext3 field i)

Defined in ZkFold.Symbolic.Data.Eq

Associated Types

type BooleanOf (Ext3 field i)

Methods

(==) :: Ext3 field i -> Ext3 field i -> BooleanOf (Ext3 field i)

(/=) :: Ext3 field i -> Ext3 field i -> BooleanOf (Ext3 field i)

Field (Ext3 f e) => Exponent (Ext3 f e) Integer

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(^) :: Ext3 f e -> Integer -> Ext3 f e

MultiplicativeMonoid (Ext3 f e) => Exponent (Ext3 f e) Natural

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

(^) :: Ext3 f e -> Natural -> Ext3 f e

FromConstant (Ext3 f e) (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

fromConstant :: Ext3 f e -> Ext3 f e

(Field f, Eq f, IrreduciblePoly f e) => Scale (Ext3 f e) (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

Methods

scale :: Ext3 f e -> Ext3 f e -> Ext3 f e

type Rep (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

type Rep (Ext3 f e) = D1 ('MetaData "Ext3" "ZkFold.Base.Algebra.Basic.Field" "symbolic-base-0.1.0.0-inplace" 'False) (C1 ('MetaCons "Ext3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 f) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 f) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 f))))

type Order (Ext3 f e)

Defined in ZkFold.Base.Algebra.Basic.Field

type Order (Ext3 f e) = Order f ^ 3

type BooleanOf (Ext3 field i)

Defined in ZkFold.Symbolic.Data.Eq

type BooleanOf (Ext3 field i) = GBooleanOf (Rep (Ext3 field i))