Bulletproofs.ArithmeticCircuit.Internal

Documentation

data ArithCircuitProofError

Constructors

TooManyGates Integer

The number of gates is too high

NNotPowerOf2 Integer

The number of gates is not a power of 2

Instances

Eq ArithCircuitProofError

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

(==) :: ArithCircuitProofError -> ArithCircuitProofError -> Bool

(/=) :: ArithCircuitProofError -> ArithCircuitProofError -> Bool

Show ArithCircuitProofError

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

showsPrec :: Int -> ArithCircuitProofError -> ShowS

show :: ArithCircuitProofError -> String

showList :: [ArithCircuitProofError] -> ShowS

data ArithCircuitProof f

Constructors

ArithCircuitProof

Fields

• tBlinding :: f

  Blinding factor of the T1 and T2 commitments, combined into the form required to make the committed version of the x-polynomial add up

• mu :: f

  Blinding factor required for the Verifier to verify commitments A, S

• t :: f

  Dot product of vectors l and r that prove knowledge of the value in range t = t(x) = l(x) · r(x)

• aiCommit :: Point

  Commitment to vectors aL and aR

• aoCommit :: Point

  Commitment to vectors aO

• sCommit :: Point

  Commitment to new vectors sL, sR, created at random by the Prover

• tCommits :: [Point]

  Commitments to t1, t3, t4, t5, t6

• productProof :: InnerProductProof f

Instances

Eq f => Eq (ArithCircuitProof f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

(==) :: ArithCircuitProof f -> ArithCircuitProof f -> Bool

(/=) :: ArithCircuitProof f -> ArithCircuitProof f -> Bool

Show f => Show (ArithCircuitProof f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

showsPrec :: Int -> ArithCircuitProof f -> ShowS

show :: ArithCircuitProof f -> String

showList :: [ArithCircuitProof f] -> ShowS

Generic (ArithCircuitProof f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Associated Types

type Rep (ArithCircuitProof f) :: Type -> Type

Methods

from :: ArithCircuitProof f -> Rep (ArithCircuitProof f) x

to :: Rep (ArithCircuitProof f) x -> ArithCircuitProof f

NFData f => NFData (ArithCircuitProof f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

rnf :: ArithCircuitProof f -> ()

type Rep (ArithCircuitProof f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

type Rep (ArithCircuitProof f) = D1 (MetaData "ArithCircuitProof" "Bulletproofs.ArithmeticCircuit.Internal" "bulletproofs-1.0.1-19OL1KfDIOwGdlR0HXS25a" False) (C1 (MetaCons "ArithCircuitProof" PrefixI True) (((S1 (MetaSel (Just "tBlinding") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 f) :*: S1 (MetaSel (Just "mu") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 f)) :*: (S1 (MetaSel (Just "t") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 f) :*: S1 (MetaSel (Just "aiCommit") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Point))) :*: ((S1 (MetaSel (Just "aoCommit") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Point) :*: S1 (MetaSel (Just "sCommit") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Point)) :*: (S1 (MetaSel (Just "tCommits") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [Point]) :*: S1 (MetaSel (Just "productProof") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (InnerProductProof f))))))

data ArithCircuit f

Constructors

ArithCircuit

Fields

• weights :: GateWeights f

  Weights for vectors of left and right inputs and for vector of outputs

• commitmentWeights :: [[f]]

  Weigths for a commitments V of rank m

• cs :: [f]

  Vector of constants of size Q

Instances

Eq f => Eq (ArithCircuit f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

(==) :: ArithCircuit f -> ArithCircuit f -> Bool

(/=) :: ArithCircuit f -> ArithCircuit f -> Bool

Show f => Show (ArithCircuit f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

showsPrec :: Int -> ArithCircuit f -> ShowS

show :: ArithCircuit f -> String

showList :: [ArithCircuit f] -> ShowS

Generic (ArithCircuit f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Associated Types

type Rep (ArithCircuit f) :: Type -> Type

Methods

from :: ArithCircuit f -> Rep (ArithCircuit f) x

to :: Rep (ArithCircuit f) x -> ArithCircuit f

KnownNat p => Arbitrary (ArithCircuit (PrimeField p))

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

arbitrary :: Gen (ArithCircuit (PrimeField p))

shrink :: ArithCircuit (PrimeField p) -> [ArithCircuit (PrimeField p)]

NFData f => NFData (ArithCircuit f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

rnf :: ArithCircuit f -> ()

type Rep (ArithCircuit f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

type Rep (ArithCircuit f) = D1 (MetaData "ArithCircuit" "Bulletproofs.ArithmeticCircuit.Internal" "bulletproofs-1.0.1-19OL1KfDIOwGdlR0HXS25a" False) (C1 (MetaCons "ArithCircuit" PrefixI True) (S1 (MetaSel (Just "weights") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (GateWeights f)) :*: (S1 (MetaSel (Just "commitmentWeights") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [[f]]) :*: S1 (MetaSel (Just "cs") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [f]))))

data GateWeights f

Constructors

GateWeights

Fields

• wL :: [[f]]

  WL ∈ F^(Q x n)

• wR :: [[f]]

  WR ∈ F^(Q x n)

• wO :: [[f]]

  WO ∈ F^(Q x n)

Instances

Eq f => Eq (GateWeights f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

(==) :: GateWeights f -> GateWeights f -> Bool

(/=) :: GateWeights f -> GateWeights f -> Bool

Show f => Show (GateWeights f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

showsPrec :: Int -> GateWeights f -> ShowS

show :: GateWeights f -> String

showList :: [GateWeights f] -> ShowS

Generic (GateWeights f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Associated Types

type Rep (GateWeights f) :: Type -> Type

Methods

from :: GateWeights f -> Rep (GateWeights f) x

to :: Rep (GateWeights f) x -> GateWeights f

NFData f => NFData (GateWeights f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

rnf :: GateWeights f -> ()

type Rep (GateWeights f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

type Rep (GateWeights f) = D1 (MetaData "GateWeights" "Bulletproofs.ArithmeticCircuit.Internal" "bulletproofs-1.0.1-19OL1KfDIOwGdlR0HXS25a" False) (C1 (MetaCons "GateWeights" PrefixI True) (S1 (MetaSel (Just "wL") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [[f]]) :*: (S1 (MetaSel (Just "wR") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [[f]]) :*: S1 (MetaSel (Just "wO") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [[f]]))))

data ArithWitness f

Constructors

ArithWitness

Fields

• assignment :: Assignment f

  Vectors of left and right inputs and vector of outputs

• commitments :: [Point]

  Vector of commited input values ∈ F^m

• commitBlinders :: [f]

  Vector of blinding factors for input values ∈ F^m

Instances

Eq f => Eq (ArithWitness f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

(==) :: ArithWitness f -> ArithWitness f -> Bool

(/=) :: ArithWitness f -> ArithWitness f -> Bool

Show f => Show (ArithWitness f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

showsPrec :: Int -> ArithWitness f -> ShowS

show :: ArithWitness f -> String

showList :: [ArithWitness f] -> ShowS

Generic (ArithWitness f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Associated Types

type Rep (ArithWitness f) :: Type -> Type

Methods

from :: ArithWitness f -> Rep (ArithWitness f) x

to :: Rep (ArithWitness f) x -> ArithWitness f

KnownNat p => Arbitrary (ArithWitness (PrimeField p))

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

arbitrary :: Gen (ArithWitness (PrimeField p))

shrink :: ArithWitness (PrimeField p) -> [ArithWitness (PrimeField p)]

NFData f => NFData (ArithWitness f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

rnf :: ArithWitness f -> ()

type Rep (ArithWitness f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

type Rep (ArithWitness f) = D1 (MetaData "ArithWitness" "Bulletproofs.ArithmeticCircuit.Internal" "bulletproofs-1.0.1-19OL1KfDIOwGdlR0HXS25a" False) (C1 (MetaCons "ArithWitness" PrefixI True) (S1 (MetaSel (Just "assignment") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Assignment f)) :*: (S1 (MetaSel (Just "commitments") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [Point]) :*: S1 (MetaSel (Just "commitBlinders") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [f]))))

data Assignment f

Constructors

Assignment

Fields

• aL :: [f]

  aL ∈ F^n. Vector of left inputs of each multiplication gate

• aR :: [f]

  aR ∈ F^n. Vector of right inputs of each multiplication gate

• aO :: [f]

  aO ∈ F^n. Vector of outputs of each multiplication gate

Instances

Eq f => Eq (Assignment f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

(==) :: Assignment f -> Assignment f -> Bool

(/=) :: Assignment f -> Assignment f -> Bool

Show f => Show (Assignment f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

showsPrec :: Int -> Assignment f -> ShowS

show :: Assignment f -> String

showList :: [Assignment f] -> ShowS

Generic (Assignment f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Associated Types

type Rep (Assignment f) :: Type -> Type

Methods

from :: Assignment f -> Rep (Assignment f) x

to :: Rep (Assignment f) x -> Assignment f

KnownNat p => Arbitrary (Assignment (PrimeField p))

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

arbitrary :: Gen (Assignment (PrimeField p))

shrink :: Assignment (PrimeField p) -> [Assignment (PrimeField p)]

NFData f => NFData (Assignment f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

Methods

rnf :: Assignment f -> ()

type Rep (Assignment f)

Defined in Bulletproofs.ArithmeticCircuit.Internal

type Rep (Assignment f) = D1 (MetaData "Assignment" "Bulletproofs.ArithmeticCircuit.Internal" "bulletproofs-1.0.1-19OL1KfDIOwGdlR0HXS25a" False) (C1 (MetaCons "Assignment" PrefixI True) (S1 (MetaSel (Just "aL") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [f]) :*: (S1 (MetaSel (Just "aR") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [f]) :*: S1 (MetaSel (Just "aO") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 [f]))))

padCircuit :: Num f => ArithCircuit f -> ArithCircuit f

Pad circuit weights to make n be a power of 2, which is required to compute the inner product proof

padAssignment :: Num f => Assignment f -> Assignment f

Pad assignment vectors to make their length n be a power of 2, which is required to compute the inner product proof

delta :: KnownNat p => Integer -> PrimeField p -> [PrimeField p] -> [PrimeField p] -> PrimeField p

commitBitVector :: KnownNat p => PrimeField p -> [PrimeField p] -> [PrimeField p] -> Point

shamirGxGxG :: (Show f, Num f) => Point -> Point -> Point -> f

shamirGs :: (Show f, Num f) => [Point] -> f

shamirZ :: (Show f, Num f) => f -> f

evaluatePolynomial :: Num f => Integer -> [[f]] -> f -> [f]

multiplyPoly :: Num n => [[n]] -> [[n]] -> [n]

vectorMatrixProduct :: Num f => [f] -> [[f]] -> [f]

vectorMatrixProductT :: Num f => [f] -> [[f]] -> [f]

matrixVectorProduct :: Num f => [[f]] -> [f] -> [f]

powerMatrix :: Num f => [[f]] -> Integer -> [[f]]

matrixProduct :: Num a => [[a]] -> [[a]] -> [[a]]

insertAt :: Int -> a -> [a] -> [a]

genIdenMatrix :: Num f => Integer -> [[f]]

genZeroMatrix :: Num f => Integer -> Integer -> [[f]]

computeInputValues :: KnownNat p => GateWeights (PrimeField p) -> [[PrimeField p]] -> Assignment (PrimeField p) -> [PrimeField p] -> [PrimeField p]

gaussianReduce :: KnownNat p => [[PrimeField p]] -> [[PrimeField p]]

substituteMatrix :: KnownNat p => [[PrimeField p]] -> [PrimeField p]

solveLinearSystem :: KnownNat p => [[PrimeField p]] -> [PrimeField p]

arithCircuitGen :: forall p. KnownNat p => Integer -> Integer -> Gen (ArithCircuit (PrimeField p))

arithAssignmentGen :: KnownNat p => Integer -> Gen (Assignment (PrimeField p))

arithWitnessGen :: KnownNat p => Assignment (PrimeField p) -> ArithCircuit (PrimeField p) -> Integer -> Gen (ArithWitness (PrimeField p))