Safe Haskell	Safe-Inferred
Language	Haskell2010

ZkFold.Symbolic.Data.FieldElement

Documentation

newtype FieldElement c Source #

Constructors

FieldElement
Fields fromFieldElement :: c Par1

Instances

Instances details

(Symbolic c, FromConstant k (BaseField c)) => FromConstant k (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods fromConstant :: k -> FieldElement c Source #
(Symbolic c, Scale k (BaseField c)) => Scale k (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods scale :: k -> FieldElement c -> FieldElement c Source #
Generic (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type Rep (FieldElement c) :: Type -> Type # Methods from :: FieldElement c -> Rep (FieldElement c) x # to :: Rep (FieldElement c) x -> FieldElement c #
Show (c Par1) => Show (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods showsPrec :: Int -> FieldElement c -> ShowS # show :: FieldElement c -> String # showList :: [FieldElement c] -> ShowS #
NFData (c Par1) => NFData (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods rnf :: FieldElement c -> () #
Eq (c Par1) => Eq (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (==) :: FieldElement c -> FieldElement c -> Bool # (/=) :: FieldElement c -> FieldElement c -> Bool #
Ord (c Par1) => Ord (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods compare :: FieldElement c -> FieldElement c -> Ordering # (<) :: FieldElement c -> FieldElement c -> Bool # (<=) :: FieldElement c -> FieldElement c -> Bool # (>) :: FieldElement c -> FieldElement c -> Bool # (>=) :: FieldElement c -> FieldElement c -> Bool # max :: FieldElement c -> FieldElement c -> FieldElement c # min :: FieldElement c -> FieldElement c -> FieldElement c #
Symbolic c => AdditiveGroup (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (-) :: FieldElement c -> FieldElement c -> FieldElement c Source # negate :: FieldElement c -> FieldElement c Source #
Symbolic c => AdditiveMonoid (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods zero :: FieldElement c Source #
Symbolic c => AdditiveSemigroup (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (+) :: FieldElement c -> FieldElement c -> FieldElement c Source #
Symbolic c => BinaryExpansion (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type Bits (FieldElement c) Source # Methods binaryExpansion :: FieldElement c -> Bits (FieldElement c) Source # fromBinary :: Bits (FieldElement c) -> FieldElement c Source #
Symbolic c => Field (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (//) :: FieldElement c -> FieldElement c -> FieldElement c Source # finv :: FieldElement c -> FieldElement c Source # rootOfUnity :: Natural -> Maybe (FieldElement c) Source #
(KnownNat (Order (FieldElement c)), KnownNat (NumberOfBits (FieldElement c))) => Finite (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type Order (FieldElement c) :: Natural Source #
Symbolic c => MultiplicativeMonoid (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods one :: FieldElement c Source #
Symbolic c => MultiplicativeSemigroup (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (*) :: FieldElement c -> FieldElement c -> FieldElement c Source #
Symbolic c => Ring (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement
Symbolic c => Semiring (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement
SymbolicData (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Associated Types type Context (FieldElement c) :: (Type -> Type) -> Type Source # type Support (FieldElement c) Source # type Layout (FieldElement c) :: Type -> Type Source # Methods pieces :: FieldElement c -> Support (FieldElement c) -> Context (FieldElement c) (Layout (FieldElement c)) Source # restore :: (Support (FieldElement c) -> Context (FieldElement c) (Layout (FieldElement c))) -> FieldElement c Source #
Symbolic c => SymbolicInput (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods isValid :: FieldElement c -> Bool (Context (FieldElement c)) Source #
Symbolic c => Exponent (FieldElement c) Integer Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (^) :: FieldElement c -> Integer -> FieldElement c Source #
Symbolic c => Exponent (FieldElement c) Natural Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (^) :: FieldElement c -> Natural -> FieldElement c Source #
FromConstant (FieldElement c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods fromConstant :: FieldElement c -> FieldElement c Source #
Symbolic c => Scale (FieldElement c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods scale :: FieldElement c -> FieldElement c -> FieldElement c Source #
Symbolic c => Eq (Bool c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (==) :: FieldElement c -> FieldElement c -> Bool c Source # (/=) :: FieldElement c -> FieldElement c -> Bool c Source #
Symbolic c => Ord (Bool c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement Methods (<=) :: FieldElement c -> FieldElement c -> Bool c Source # (<) :: FieldElement c -> FieldElement c -> Bool c Source # (>=) :: FieldElement c -> FieldElement c -> Bool c Source # (>) :: FieldElement c -> FieldElement c -> Bool c Source # max :: FieldElement c -> FieldElement c -> FieldElement c Source # min :: FieldElement c -> FieldElement c -> FieldElement c Source #
(Symbolic ctx, EllipticCurve c, SymbolicData (Point c), Context (Point c) ~ ctx, PedersonSetup (Point c), Layout (Point c) ~ l, Representable l, Traversable l) => HomomorphicCommit (FieldElement ctx) (FieldElement ctx) (Point c) Source #	Pedersen commitment scheme Commitment key consists of field elements g and h, and randomness r
Instance details Defined in ZkFold.Base.Protocol.Protostar.Commit Methods hcommit :: FieldElement ctx -> FieldElement ctx -> Point c Source #
(EllipticCurve c, SymbolicData (Point c), l ~ Layout (Point c), Representable l, Traversable l, ctx ~ Context (Point c), Symbolic ctx, a ~ BaseField ctx, bits ~ NumberOfBits a) => Scale (FieldElement ctx) (Point c) Source #
Instance details Defined in ZkFold.Symbolic.Data.Ed25519 Methods scale :: FieldElement ctx -> Point c -> Point c Source #
(Symbolic c, NumberOfBits (BaseField c) ~ n) => Iso (FieldElement c) (ByteString n c) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods from :: FieldElement c -> ByteString n c Source #
(Arithmetic a, Symbolic ctx, FromConstant a (BaseField ctx), Scale a (BaseField ctx)) => SpecialSoundProtocol (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source #
Instance details Defined in ZkFold.Base.Protocol.Protostar.ArithmeticCircuit Associated Types type Witness (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source # type Input (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source # type ProverMessage (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source # type VerifierMessage (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source # type VerifierOutput (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source # type Degree (ArithmeticCircuit a (Vector n) o) :: Natural Source # Methods outputLength :: ArithmeticCircuit a (Vector n) o -> Natural Source # rounds :: ArithmeticCircuit a (Vector n) o -> Natural Source # prover :: ArithmeticCircuit a (Vector n) o -> Witness (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) -> Input (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) -> SpecialSoundTranscript (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) -> ProverMessage (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source # verifier :: ArithmeticCircuit a (Vector n) o -> Input (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) -> [ProverMessage (FieldElement ctx) (ArithmeticCircuit a (Vector n) o)] -> [FieldElement ctx] -> VerifierOutput (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source #
(Symbolic c, KnownRegisterSize r, NumberOfBits (BaseField c) ~ n) => Iso (FieldElement c) (UInt n r c) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods from :: FieldElement c -> UInt n r c Source #
(Symbolic c, NumberOfBits (BaseField c) ~ n) => Iso (ByteString n c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.ByteString Methods from :: ByteString n c -> FieldElement c Source #
(Symbolic c, KnownRegisterSize r, NumberOfBits (BaseField c) ~ n) => Iso (UInt n r c) (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.UInt Methods from :: UInt n r c -> FieldElement c Source #
type Rep (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Rep (FieldElement c) = D1 ('MetaData "FieldElement" "ZkFold.Symbolic.Data.FieldElement" "symbolic-base-0.1.0.0-inplace" 'True) (C1 ('MetaCons "FieldElement" 'PrefixI 'True) (S1 ('MetaSel ('Just "fromFieldElement") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (c Par1))))
type Bits (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Bits (FieldElement c) = c (Vector (NumberOfBits (BaseField c)))
type Order (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Order (FieldElement c) = Order (BaseField c)
type Context (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Context (FieldElement c) = Context (c Par1)
type Layout (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Layout (FieldElement c) = Layout (c Par1)
type Support (FieldElement c) Source #
Instance details Defined in ZkFold.Symbolic.Data.FieldElement type Support (FieldElement c) = Support (c Par1)
type Input (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source #
Instance details Defined in ZkFold.Base.Protocol.Protostar.ArithmeticCircuit type Input (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) = Vector n (FieldElement ctx)
type ProverMessage (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source #
Instance details Defined in ZkFold.Base.Protocol.Protostar.ArithmeticCircuit type ProverMessage (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) = Map ByteString (FieldElement ctx)
type VerifierMessage (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source #
Instance details Defined in ZkFold.Base.Protocol.Protostar.ArithmeticCircuit type VerifierMessage (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) = FieldElement ctx
type VerifierOutput (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source #
Instance details Defined in ZkFold.Base.Protocol.Protostar.ArithmeticCircuit type VerifierOutput (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) = Bool ctx
type Witness (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) Source #
Instance details Defined in ZkFold.Base.Protocol.Protostar.ArithmeticCircuit type Witness (FieldElement ctx) (ArithmeticCircuit a (Vector n) o) = (Vector n a, Map ByteString a)