proof_system::honk::pcs::shplonk Namespace Reference

Reduces multiple claims about commitments, each opened at a single point into a single claim for a single polynomial opened at a single point. More...

Classes
struct	ProverOutput
	Prover output (claim=([G], r, 0), witness = G(X), proof = [Q]) that can be passed on to a univariate opening protocol. More...
class	ShplonkProver_
	Shplonk Prover. More...
class	ShplonkTest
class	ShplonkVerifier_
	Shplonk Verifier. More...

Typedefs
template<typename Curve >
using	OutputWitness = barretenberg::Polynomial< typename Curve::ScalarField >
	Polynomial G(X) = Q(X) - ∑ₖ ẑₖ(r)⋅( Bₖ(X) − Tₖ(z) ), where Q(X) = ∑ₖ ( Bₖ(X) − Tₖ(X) ) / zₖ(X)
using	CurveTypes = ::testing::Types< curve::BN254, curve::Grumpkin >

Functions
	TYPED_TEST_SUITE (ShplonkTest, CurveTypes)
	TYPED_TEST (ShplonkTest, ShplonkSimple)

Detailed Description

Reduces multiple claims about commitments, each opened at a single point into a single claim for a single polynomial opened at a single point.

We use the following terminology:

• Bₖ(X) is a random linear combination of all polynomials opened at Ωₖ we refer to it a 'merged_polynomial'.
• Tₖ(X) is the polynomial that interpolates Bₖ(X) over Ωₖ,
• zₖ(X) is the product of all (X-x), for x ∈ Ωₖ
• ẑₖ(X) = 1/zₖ(X)

The challenges are ρ (batching) and r (random evaluation).

Typedef Documentation

OutputWitness

template<typename Curve >

using proof_system::honk::pcs::shplonk::OutputWitness = typedef barretenberg::Polynomial<typename Curve::ScalarField>

Polynomial G(X) = Q(X) - ∑ₖ ẑₖ(r)⋅( Bₖ(X) − Tₖ(z) ), where Q(X) = ∑ₖ ( Bₖ(X) − Tₖ(X) ) / zₖ(X)

Template Parameters

Curve

EC parameters