The implementation of the sumcheck Prover for statements of the form \(\sum_{\vec \ell \in \{0,1\}^d} pow_{\beta}(\vec \ell) \cdot F \left(P_1(\vec \ell),\ldots, P_N(\vec \ell) \right) = 0 \) for multilinear polynomials \(P_1, \ldots, P_N \). More...

#include <sumcheck.hpp>

Public Types
using	FF = typename Flavor::FF

using	ProverPolynomials = typename Flavor::ProverPolynomials

using	PartiallyEvaluatedMultivariates = typename Flavor::PartiallyEvaluatedMultivariates

using	ClaimedEvaluations = typename Flavor::AllValues

using	ZKData = ZKSumcheckData< Flavor >

using	Transcript = typename Flavor::Transcript

using	SubrelationSeparators = std::array< FF, Flavor::NUM_SUBRELATIONS - 1 >

using	CommitmentKey = typename Flavor::CommitmentKey

using	SumcheckRoundUnivariate = typename bb::Univariate< FF, BATCHED_RELATION_PARTIAL_LENGTH >

Public Member Functions
	SumcheckProver (size_t multivariate_n, ProverPolynomials &prover_polynomials, std::shared_ptr< Transcript > transcript, const FF &relation_separator, const size_t virtual_log_n, const std::vector< FF > &accumulator_challenge, const std::vector< FF > &instance_challenge)

	SumcheckProver (size_t multivariate_n, ProverPolynomials &prover_polynomials, std::shared_ptr< Transcript > transcript, const FF &alpha, const std::vector< FF > &gate_challenges, const RelationParameters< FF > &relation_parameters, const size_t virtual_log_n)

SumcheckOutput< Flavor >	prove ()
	Non-ZK version: Compute round univariate, place it in transcript, compute challenge, partially evaluate. Repeat until final round, then get full evaluations of prover polynomials, and place them in transcript.

template<typename PolynomialT , std::size_t N>
void	partially_evaluate (std::array< PolynomialT, N > &polynomials, const FF &round_challenge)
	Evaluate at the round challenge and prepare class for next round. Specialization for array, see generic version.

ClaimedEvaluations	extract_claimed_evaluations (PartiallyEvaluatedMultivariates &partially_evaluated_polynomials)
	This method takes the book-keeping table containing partially evaluated prover polynomials and creates a vector containing the evaluations of all prover polynomials at the point \( (u_0, \ldots, u_{d-1} )\). For ZK Flavors: this method takes the book-keeping table containing partially evaluated prover polynomials and creates a vector containing the evaluations of all witness polynomials at the point \( (u_0, \ldots, u_{d-1} )\) masked by the terms \( \texttt{eval_masking_scalars}_j\cdot \sum u_i(1-u_i)\) and the evaluations of all non-witness polynomials that are sent in clear.

Public Attributes
const size_t	multivariate_n

const size_t	multivariate_d

ProverPolynomials &	full_polynomials

std::shared_ptr< Transcript >	transcript

SumcheckProverRound< Flavor >	round

SubrelationSeparators	alphas

std::vector< FF >	gate_challenges

bb::RelationParameters< FF >	relation_parameters

size_t	virtual_log_n

std::vector< FF >	multivariate_challenge

std::vector< FF >	accumulator_challenge = {}

std::vector< FF >	instance_challenge = {}

FF	libra_evaluation = FF{ 0 }

RowDisablingPolynomial< FF >	row_disabling_polynomial

PartiallyEvaluatedMultivariates	partially_evaluated_polynomials
	Container for partially evaluated Prover Polynomials at a current challenge. Upon computing challenge \( u_i \), the first \(2^{d-1-i}\) rows are updated using partially evaluate method.

SumcheckOutput< Flavor > prove(ZKData &zk_sumcheck_data) void	partially_evaluate (auto &polynomials, const FF &round_challenge)
	ZK-version of `prove` that runs Sumcheck with disabled rows and masking of Round Univariates. The masking is ensured by adding random Libra univariates to the Sumcheck round univariates.

Static Public Attributes
static constexpr bool	isMultilinearBatchingFlavor = IsAnyOf<Flavor, MultilinearBatchingFlavor>

static constexpr size_t	MAX_PARTIAL_RELATION_LENGTH = Flavor::MAX_PARTIAL_RELATION_LENGTH
	The total algebraic degree of the Sumcheck relation \( F \) as a polynomial in Prover Polynomials \(P_1,\ldots, P_N\).

static constexpr size_t	BATCHED_RELATION_PARTIAL_LENGTH = Flavor::BATCHED_RELATION_PARTIAL_LENGTH

Detailed Description

template<typename Flavor>
class bb::SumcheckProver< Flavor >

The implementation of the sumcheck Prover for statements of the form \(\sum_{\vec \ell \in \{0,1\}^d} pow_{\beta}(\vec \ell) \cdot F \left(P_1(\vec \ell),\ldots, P_N(\vec \ell) \right) = 0 \) for multilinear polynomials \(P_1, \ldots, P_N \).

Notation and Setup

Obtaining Prover/Honk Polynomials

The Sumcheck is applied to multivariate polynomials \(P_1, \ldots, P_N\) that are specidied by Flavor. Namely, prove method obtains full_polynomials by reference from Flavor 's prover polynomials. In particular, their number \(N\) is specified by the Flavor.

Sumcheck Relation

Given multilinear polynomials \( P_1,\ldots, P_N \in \mathbb{F}[X_0,\ldots, X_{d-1}] \) and a relation \( F \) which is a polynomial in \( N \) variables, we use Sumcheck over the polynomial

\begin{align} \tilde{F} (X_0,\ldots, X_{d-1}) = pow_{\beta}(X_0,\ldots, X_{d-1}) \cdot F\left( P_1 (X_0,\ldots, X_{d-1}), \ldots, P_N (X_0,\ldots, X_{d-1}) \right) \end{align}

to establish that \( F(P_1(\vec \ell),\ldots, P_N(\vec \ell) ) = 0 \), i.e. that \( F \) is satisfied, at every point of \(\{0,1\}^d\).

In the implementation, the relation polynomial \( F \) is determined by Flavor::Relations which is fed to Sumcheck Round Prover.

Input and Parameters

The following constants are used:

\( d \) the number of variables in the multilinear polynomials
\( n \) the size of the hypercube, i.e. \( 2^d\).
\( D = \) total degree of \(\tilde{F}\) as a polynomial in \(P_1,\ldots, P_N\) incremented by 1.

Honk Polynomials and Partially Evaluated Polynomials

Given \( N \) Honk Prover Polynomials \( P_1, \ldots, P_N \), i.e. multilinear polynomials in \( d \) variables.

Round 0

At initialization, Prover Polynomials are submitted by reference into full_polynomials, which is a two-dimensional array with \(N\) columns and \(2^d\) rows, whose entries are defined as follows \(\texttt{full_polynomials}_{i,j} = P_j(\vec i) \). Here, \( \vec i \in \{0,1\}^d \) is identified with the binary representation of the integer \( 0 \leq i \leq 2^d-1 \).

When the first challenge \( u_0 \) is computed, the method partially evaluate takes as input full_polynomials and populates a new book-keeping table denoted by \(\texttt{partially_evaluated_polynomials} \). Its \( n/2 = 2^{d-1} \) rows will represent the evaluations \( P_i(u_0, X_1, ..., X_{d-1}) \), which are multilinear polynomials in \( d-1 \) variables.

More precisely, it is a table with \( 2^{d-1} \) rows and \( N \) columns, such that

\begin{align} \texttt{partially_evaluated_polynomials}_{i,j} = &\ P_j(0, i_1,\ldots, i_{d-1}) + u_0 \cdot (P_j(1,i_1,\ldots, i_{d-1})) - P_j(0, i_1,\ldots, i_{d-1})) \\ = &\ \texttt{full_polynomials}_{2 i,j} + u_0 \cdot (\texttt{full_polynomials}_{2i+1,j} - \texttt{full_polynomials}_{2 i,j}) \end{align}

Updating Partial Evaluations in Subsequent Rounds

In Round \( i < d-1\), partially evaluate updates the first \( 2^{d-1 - i} \) rows of \(\texttt{partially_evaluated_polynomials}\) with the evaluations \( P_1(u_0,\ldots, u_i, \vec \ell),\ldots, P_N(u_0,\ldots, u_i, \vec \ell)\) for \(\vec \ell \in \{0,1\}^{d-1-i}\). The details are specified in the corresponding docs.

Final Step

After computing the last challenge \( u_{d-1} \) in Round \( d-1 \) and updating \( \texttt{partially_evaluated_polynomials} \), the prover looks into the 'top' row of the table containing evaluations \(P_1(u_0,\ldots, u_{d-1}), \ldots, P_N(u_0,\ldots, u_{d-1})\) and concatenates these values with the last challenge to the transcript.

Round Univariates

Contributions of GateSeparatorPolynomial

Let \( \vec \beta = (\beta_0,\ldots, \beta_{d-1}) \in \mathbb{F}\) be a vector of challenges.

In Round \(i\), a univariate polynomial \( \tilde S^{i}(X_{i}) \) for the relation defined by \( \tilde{F}(X)\) is computed as follows. First, we introduce notation

\( c_i = pow_{\beta}(u_0,\ldots, u_{i-1}) \)
\( T^{i}( X_i ) = \sum_{ \ell = 0} ^{2^{d-i-1}-1} \beta_{i+1}^{\ell_{i+1}} \cdot \ldots \cdot \beta_{d-1}^{\ell_{d-1}} \cdot S^i_{\ell}( X_i ) \)
\( S^i_{\ell} (X_i) = F \left(P_1(u_0,\ldots, u_{i-1}, X_i, \vec \ell), \ldots, P_1(u_0,\ldots, u_{i-1}, X_i, \vec \ell) \right) \)

As explained in GateSeparatorPolynomial,

\begin{align} \tilde{S}^{i}(X_i) = \sum_{ \ell = 0} ^{2^{d-i-1}-1} pow^i_\beta ( X_i, \ell_{i+1}, \ldots, \ell_{d-1} ) \cdot S^i_{\ell}( X_i ) = c_i\cdot ( (1−X_i) + X_i\cdot \beta_i ) \cdot \sum_{\ell = 0}^{2^{d-i-1}-1} \beta_{i+1}^{\ell_{i+1}} \cdot \ldots \cdot \beta_{d-1}^{\ell_{d-1}} \cdot S^{i}_{\ell}( X_i ). \end{align}

Computing Round Univariates

The evaluations of the round univariate \( \tilde{S}^i \) over the domain \(0,\ldots, D \) are obtained by the method compute_univariate. The implementation consists of the following sub-methods:

Extend evaluations of linear univariate polynomials \( P_j(u_0,\ldots, u_{i-1}, X_i, \vec \ell) \) to the domain \(0,\ldots, D\).
Accumulate per-relation contributions of the extended polynomials to \( T^i(X_i)\)
Extend and batch the subrelation contibutions multiplying by the constants \(c_i\) and the evaluations of \( ( (1−X_i) + X_i\cdot \beta_i ) \).

Transcript Operations

After computing Round univariates and adding them to the transcript, the prover generates round challenge by hashing the transcript. These operations are taken care of by Transcript Class methods.

Output

The Sumcheck output is specified by bb::SumcheckOutput< Flavor >.

Definition at line 289 of file sumcheck.hpp.

Member Typedef Documentation

◆ ClaimedEvaluations

template<typename Flavor >

using bb::SumcheckProver< Flavor >::ClaimedEvaluations = typename Flavor::AllValues

Definition at line 296 of file sumcheck.hpp.

◆ CommitmentKey

template<typename Flavor >

using bb::SumcheckProver< Flavor >::CommitmentKey = typename Flavor::CommitmentKey

Definition at line 300 of file sumcheck.hpp.

◆ FF

template<typename Flavor >

using bb::SumcheckProver< Flavor >::FF = typename Flavor::FF

Definition at line 291 of file sumcheck.hpp.

◆ PartiallyEvaluatedMultivariates

template<typename Flavor >

using bb::SumcheckProver< Flavor >::PartiallyEvaluatedMultivariates = typename Flavor::PartiallyEvaluatedMultivariates

Definition at line 295 of file sumcheck.hpp.

◆ ProverPolynomials

template<typename Flavor >

using bb::SumcheckProver< Flavor >::ProverPolynomials = typename Flavor::ProverPolynomials

Definition at line 294 of file sumcheck.hpp.

◆ SubrelationSeparators

template<typename Flavor >

using bb::SumcheckProver< Flavor >::SubrelationSeparators = std::array<FF, Flavor::NUM_SUBRELATIONS - 1>

Definition at line 299 of file sumcheck.hpp.

◆ SumcheckRoundUnivariate

template<typename Flavor >

using bb::SumcheckProver< Flavor >::SumcheckRoundUnivariate = typename bb::Univariate<FF, BATCHED_RELATION_PARTIAL_LENGTH>

Definition at line 312 of file sumcheck.hpp.

◆ Transcript

template<typename Flavor >

using bb::SumcheckProver< Flavor >::Transcript = typename Flavor::Transcript

Definition at line 298 of file sumcheck.hpp.

◆ ZKData

template<typename Flavor >

using bb::SumcheckProver< Flavor >::ZKData = ZKSumcheckData<Flavor>

Definition at line 297 of file sumcheck.hpp.

Constructor & Destructor Documentation

◆ SumcheckProver() [1/2]

template<typename Flavor >

bb::SumcheckProver< Flavor >::SumcheckProver	(	size_t	multivariate_n,
		ProverPolynomials &	prover_polynomials,
		std::shared_ptr< Transcript >	transcript,
		const FF &	relation_separator,
		const size_t	virtual_log_n,
		const std::vector< FF > &	accumulator_challenge,
		const std::vector< FF > &	instance_challenge
	)

inline

Definition at line 356 of file sumcheck.hpp.

◆ SumcheckProver() [2/2]

template<typename Flavor >

bb::SumcheckProver< Flavor >::SumcheckProver	(	size_t	multivariate_n,
		ProverPolynomials &	prover_polynomials,
		std::shared_ptr< Transcript >	transcript,
		const FF &	alpha,
		const std::vector< FF > &	gate_challenges,
		const RelationParameters< FF > &	relation_parameters,
		const size_t	virtual_log_n
	)

inline

Definition at line 376 of file sumcheck.hpp.

Member Function Documentation

◆ extract_claimed_evaluations()

template<typename Flavor >

ClaimedEvaluations bb::SumcheckProver< Flavor >::extract_claimed_evaluations ( PartiallyEvaluatedMultivariates & partially_evaluated_polynomials )

inline

This method takes the book-keeping table containing partially evaluated prover polynomials and creates a vector containing the evaluations of all prover polynomials at the point \( (u_0, \ldots, u_{d-1} )\). For ZK Flavors: this method takes the book-keeping table containing partially evaluated prover polynomials and creates a vector containing the evaluations of all witness polynomials at the point \( (u_0, \ldots, u_{d-1} )\) masked by the terms \( \texttt{eval_masking_scalars}_j\cdot \sum u_i(1-u_i)\) and the evaluations of all non-witness polynomials that are sent in clear.

Parameters

partially_evaluated_polynomials
multivariate_evaluations

Definition at line 740 of file sumcheck.hpp.

◆ partially_evaluate()

template<typename Flavor >

template<typename PolynomialT , std::size_t N>

void bb::SumcheckProver< Flavor >::partially_evaluate	(	std::array< PolynomialT, N > &	polynomials,
		const FF &	round_challenge
	)

inline

Evaluate at the round challenge and prepare class for next round. Specialization for array, see generic version.

Definition at line 708 of file sumcheck.hpp.

◆ prove()

template<typename Flavor >

SumcheckOutput< Flavor > bb::SumcheckProver< Flavor >::prove ( )

inline

Non-ZK version: Compute round univariate, place it in transcript, compute challenge, partially evaluate. Repeat until final round, then get full evaluations of prover polynomials, and place them in transcript.

See Detailed description of Sumcheck Prover <Flavor>.

Returns: SumcheckOutput

Definition at line 398 of file sumcheck.hpp.

Member Data Documentation

◆ accumulator_challenge

template<typename Flavor >

std::vector<FF> bb::SumcheckProver< Flavor >::accumulator_challenge = {}

Definition at line 338 of file sumcheck.hpp.

◆ alphas

template<typename Flavor >

SubrelationSeparators bb::SumcheckProver< Flavor >::alphas

Definition at line 326 of file sumcheck.hpp.

◆ BATCHED_RELATION_PARTIAL_LENGTH

template<typename Flavor >

constexpr size_t bb::SumcheckProver< Flavor >::BATCHED_RELATION_PARTIAL_LENGTH = Flavor::BATCHED_RELATION_PARTIAL_LENGTH

staticconstexpr

Definition at line 310 of file sumcheck.hpp.

◆ full_polynomials

template<typename Flavor >

ProverPolynomials& bb::SumcheckProver< Flavor >::full_polynomials

Definition at line 319 of file sumcheck.hpp.

◆ gate_challenges

template<typename Flavor >

std::vector<FF> bb::SumcheckProver< Flavor >::gate_challenges

Definition at line 328 of file sumcheck.hpp.

◆ instance_challenge

template<typename Flavor >

std::vector<FF> bb::SumcheckProver< Flavor >::instance_challenge = {}

Definition at line 339 of file sumcheck.hpp.

◆ isMultilinearBatchingFlavor

template<typename Flavor >

constexpr bool bb::SumcheckProver< Flavor >::isMultilinearBatchingFlavor = IsAnyOf<Flavor, MultilinearBatchingFlavor>

staticconstexpr

Definition at line 302 of file sumcheck.hpp.

◆ libra_evaluation

template<typename Flavor >

FF bb::SumcheckProver< Flavor >::libra_evaluation = FF{ 0 }

Definition at line 340 of file sumcheck.hpp.

◆ MAX_PARTIAL_RELATION_LENGTH

template<typename Flavor >

constexpr size_t bb::SumcheckProver< Flavor >::MAX_PARTIAL_RELATION_LENGTH = Flavor::MAX_PARTIAL_RELATION_LENGTH

staticconstexpr

The total algebraic degree of the Sumcheck relation \( F \) as a polynomial in Prover Polynomials \(P_1,\ldots, P_N\).

Definition at line 307 of file sumcheck.hpp.

◆ multivariate_challenge

template<typename Flavor >

std::vector<FF> bb::SumcheckProver< Flavor >::multivariate_challenge

Definition at line 335 of file sumcheck.hpp.

◆ multivariate_d

template<typename Flavor >

const size_t bb::SumcheckProver< Flavor >::multivariate_d

Definition at line 317 of file sumcheck.hpp.

◆ multivariate_n

template<typename Flavor >

const size_t bb::SumcheckProver< Flavor >::multivariate_n

Definition at line 315 of file sumcheck.hpp.

◆ partially_evaluate

template<typename Flavor >

SumcheckOutput< Flavor > prove(ZKData &zk_sumcheck_data) void bb::SumcheckProver< Flavor >::partially_evaluate(auto &polynomials, const FF &round_challenge)

inline

ZK-version of prove that runs Sumcheck with disabled rows and masking of Round Univariates. The masking is ensured by adding random Libra univariates to the Sumcheck round univariates.

Parameters

zk_sumcheck_data

Returns: SumcheckOutput<Flavor>

Evaluate Honk polynomials at the round challenge and prepare class for next round.

At initialization, Prover Polynomials are submitted by reference into full_polynomials, which is a two-dimensional array defined as

\begin{align} \texttt{full_polynomials}_{i,j} = P_j(\vec i). \end{align}

Here, \( \vec i \in \{0,1\}^d \) is identified with the binary representation of the integer \( 0 \leq i \leq 2^d-1 \).

When the first challenge \( u_0 \) is computed, the method partially evaluate takes as input full_polynomials and populates a new book-keeping table denoted \(\texttt{partially_evaluated_polynomials}\). Its \( n/2 = 2^{d-1} \) rows represent the evaluations \( P_i(u_0, X_1, ..., X_{d-1}) \), which are multilinear polynomials in \( d-1 \) variables. More precisely, it is a table \( 2^{d-1} \) rows and \( N \) columns, such that

\begin{align} \texttt{partially_evaluated_polynomials}_{i,j} = &\ P_j(0, i_1,\ldots, i_{d-1}) + u_0 \cdot (P_j(1, i_1,\ldots, i_{d-1})) - P_j(0, i_1,\ldots, i_{d-1})) \\ = &\ \texttt{full_polynomials}_{2 i,j} + u_0 \cdot (\texttt{full_polynomials}_{2i+1,j} - \texttt{full_polynomials}_{2 i,j}) \end{align}

We elude copying all of the polynomial-defining data by only populating partially_evaluated_polynomials after the first round.

In Round \(0<i\leq d-1\), this method takes the challenge \( u_{i} \) and rewrites the first \( 2^{d-i-1} \) rows in the \( \texttt{partially_evaluated_polynomials} \) table with the values

\begin{align} \texttt{partially_evaluated_polynomials}_{\ell,j} \gets &\ P_j\left(u_0,\ldots, u_{i}, \vec \ell \right) \\ = &\ P_j\left(u_0,\ldots, u_{i-1}, 0, \vec \ell \right) + u_{i} \cdot \left( P_j\left(u_0, \ldots, u_{i-1}, 1, \vec \ell ) - P_j(u_0,\ldots, u_{i-1}, 0, \vec \ell \right)\right) \\ = &\ \texttt{partially_evaluated_polynomials}_{2 \ell,j} + u_{i} \cdot (\texttt{partially_evaluated_polynomials}_{2 \ell+1,j} - \texttt{partially_evaluated_polynomials}_{2\ell,j}) \end{align}

where \(\vec \ell \in \{0,1\}^{d-1-i}\). After the final update, i.e. when \( i = d-1 \), the upper row of the table contains the evaluations of Honk polynomials at the challenge point \( (u_0,\ldots, u_{d-1}) \).

Parameters

polynomials	Honk polynomials at initialization; partially evaluated polynomials in subsequent rounds
round_size	\(2^{d-i}\)
round_challenge	\(u_i\)

Definition at line 682 of file sumcheck.hpp.

◆ partially_evaluated_polynomials

template<typename Flavor >

PartiallyEvaluatedMultivariates bb::SumcheckProver< Flavor >::partially_evaluated_polynomials

Container for partially evaluated Prover Polynomials at a current challenge. Upon computing challenge \( u_i \), the first \(2^{d-1-i}\) rows are updated using partially evaluate method.

NOTE: With ~40 columns, prob only want to allocate 256 EdgeGroup's at once to keep stack under 1MB? TODO(#224)(Cody): might want to just do C-style multidimensional array? for guaranteed adjacency?

Definition at line 353 of file sumcheck.hpp.

◆ relation_parameters

template<typename Flavor >

bb::RelationParameters<FF> bb::SumcheckProver< Flavor >::relation_parameters

Definition at line 330 of file sumcheck.hpp.

◆ round

template<typename Flavor >

SumcheckProverRound<Flavor> bb::SumcheckProver< Flavor >::round

Definition at line 323 of file sumcheck.hpp.

◆ row_disabling_polynomial

template<typename Flavor >

RowDisablingPolynomial<FF> bb::SumcheckProver< Flavor >::row_disabling_polynomial

Definition at line 342 of file sumcheck.hpp.

◆ transcript

template<typename Flavor >

std::shared_ptr<Transcript> bb::SumcheckProver< Flavor >::transcript

Definition at line 321 of file sumcheck.hpp.

◆ virtual_log_n

template<typename Flavor >

size_t bb::SumcheckProver< Flavor >::virtual_log_n

Definition at line 333 of file sumcheck.hpp.

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

src/barretenberg/sumcheck/sumcheck.hpp

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Notation and Setup

Obtaining Prover/Honk Polynomials

Sumcheck Relation

Input and Parameters

Honk Polynomials and Partially Evaluated Polynomials

Round 0

Updating Partial Evaluations in Subsequent Rounds

Final Step

Round Univariates

Contributions of GateSeparatorPolynomial

Computing Round Univariates

Transcript Operations

Output

Member Typedef Documentation

◆ ClaimedEvaluations

◆ CommitmentKey

◆ FF

◆ PartiallyEvaluatedMultivariates

◆ ProverPolynomials

◆ SubrelationSeparators

◆ SumcheckRoundUnivariate

◆ Transcript

◆ ZKData

Constructor & Destructor Documentation

◆ SumcheckProver() [1/2]

◆ SumcheckProver() [2/2]

Member Function Documentation

◆ extract_claimed_evaluations()

◆ partially_evaluate()

◆ prove()

Member Data Documentation

◆ accumulator_challenge

◆ alphas

◆ BATCHED_RELATION_PARTIAL_LENGTH

◆ full_polynomials

◆ gate_challenges

◆ instance_challenge

◆ isMultilinearBatchingFlavor

◆ libra_evaluation

◆ MAX_PARTIAL_RELATION_LENGTH

◆ multivariate_challenge

◆ multivariate_d

◆ multivariate_n

◆ partially_evaluate

◆ partially_evaluated_polynomials

◆ relation_parameters

◆ round

◆ row_disabling_polynomial

◆ transcript

◆ virtual_log_n