Static Public Member Functions
static void	compute_opening_proof (std::shared_ptr< CK > ck, const OpeningPair< Curve > &opening_pair, const Polynomial &polynomial, const std::shared_ptr< BaseTranscript > &prover_trancript)
	Computes the KZG commitment to an opening proof polynomial at a single evaluation point.

static bool	verify (const std::shared_ptr< VK > &vk, const OpeningClaim< Curve > &claim, const std::shared_ptr< BaseTranscript > &verifier_transcript)
	Computes the KZG verification for an opening claim of a single polynomial commitment.

static std::array< GroupElement, 2 >	compute_pairing_points (const OpeningClaim< Curve > &claim, const auto &verifier_transcript)
	Computes the input points for the pairing check needed to verify a KZG opening claim of a single polynomial commitment. This reduction is non-interactive and always succeeds.

Member Function Documentation

◆ compute_opening_proof()

template<typename Curve >

static void proof_system::honk::pcs::kzg::KZG< Curve >::compute_opening_proof	(	std::shared_ptr< CK >	ck,
		const OpeningPair< Curve > &	opening_pair,
		const Polynomial &	polynomial,
		const std::shared_ptr< BaseTranscript > &	prover_trancript
	)

inlinestatic

Computes the KZG commitment to an opening proof polynomial at a single evaluation point.

Parameters

ck	The commitment key which has a commit function, the srs and pippenger_runtime_state
opening_pair	OpeningPair = {r, v = p(r)}
polynomial	The witness whose opening proof needs to be computed
prover_transcript	Prover transcript

◆ compute_pairing_points()

template<typename Curve >

static std::array< GroupElement, 2 > proof_system::honk::pcs::kzg::KZG< Curve >::compute_pairing_points	(	const OpeningClaim< Curve > &	claim,
		const auto &	verifier_transcript
	)

inlinestatic

Computes the input points for the pairing check needed to verify a KZG opening claim of a single polynomial commitment. This reduction is non-interactive and always succeeds.

This is used in the recursive setting where we want to "aggregate" proofs, not verify them.

Parameters

claim OpeningClaim ({r, v}, C)

Returns

{P₀, P₁} where

P₀ = C − v⋅[1]₁ + r⋅[W(x)]₁
P₁ = [W(x)]₁

◆ verify()

template<typename Curve >

static bool proof_system::honk::pcs::kzg::KZG< Curve >::verify	(	const std::shared_ptr< VK > &	vk,
		const OpeningClaim< Curve > &	claim,
		const std::shared_ptr< BaseTranscript > &	verifier_transcript
	)

inlinestatic

Computes the KZG verification for an opening claim of a single polynomial commitment.

Parameters

vk	is the verification key which has a pairing check function
claim	OpeningClaim ({r, v}, C)

Returns

e(P₀,[1]₁)e(P₁,[x]₂)≡ [1]ₜ where

P₀ = C − v⋅[1]₁ + r⋅[x]₁
P₁ = [Q(x)]₁

The documentation for this class was generated from the following file:

src/barretenberg/commitment_schemes/kzg/kzg.hpp

Static Public Member Functions

Member Function Documentation

◆ compute_opening_proof()

◆ compute_pairing_points()

◆ verify()