Struct SparseMultiDenseProductSumcheckProver 

pub struct SparseMultiDenseProductSumcheckProver<P: PackedField> { /* private fields */ }

Proves the hypercube sums of one sparse multilinear against several dense ones.

The sparse multilinear is shared, so it is stored once and folded once. That holds however many dense columns ride along.

One prover per column would instead hold a copy of the entry list each. Every copy would then fold each round. Avoiding that is the whole reason this exists.

One round polynomial comes out per column. The batching driver combines a prover’s polynomials exactly as it would separate provers’.

The claim each column carries is its own. So the columns are independent sums that happen to share a factor.

Everything else follows the single-column prover in this module. A test pins the two together at one column.

Implementations

impl<P: PackedField> SparseMultiDenseProductSumcheckProver<P>

pub fn new( sparse: Vec<SparseEntry<P::Scalar>>, dense: Vec<FactoredMultilinear<P>>, sums: &[P::Scalar], ) -> Self

Creates a prover for the claim that each sparse-dense product sums to its stated value.

Arguments

• sparse - entries of the shared sparse multilinear, in any order, indices repeatable.
• dense - one dense multilinear per claim, all over the same variables.
• sums - the claimed sum of each product over the hypercube.

Panics

Panics if the columns disagree on their variable count.

Panics if there is not one sum per column, or if any entry index is out of range.

Trait Implementations

impl<F: Field, P: PackedField<Scalar = F>> SumcheckProver<F> for SparseMultiDenseProductSumcheckProver<P>

fn n_vars(&self) -> usize

The number of variables in the remaining multivariate polynomial.

fn execute(&mut self) -> Vec<RoundCoeffs<F>>

Computes the prover messages for this round as a univariate polynomial.

fn fold(&mut self, challenge: F)

Folds the sumcheck multilinears with a new verifier challenge.

fn finish(self) -> Vec<F>

Finishes the sumcheck proving protocol and returns the evaluations of all multilinears at the challenge point.