Struct PaddedSumcheckDecorator 

pub struct PaddedSumcheckDecorator<F: Field, Inner> { /* private fields */ }

Decorator that pads the number of variables of an inner SumcheckProver.

Given an inner prover for the hypercube sum of an n-variate multilinear $f(X_0, \ldots, X_{n-1}) = s$, this exposes a prover over n + n_extra_vars variables for the equivalent claim

$$ f(X_0, \ldots, X_{n-1}) \cdot \text{eq}(0^{n_\text{extra}}, X_n, \ldots, X_{n+n_\text{extra}-1}) = s $$

Since $\text{eq}(0, \cdot)$ sums to 1 over the hypercube, this padded claim holds iff the original does. This is useful for batching sumchecks with unequal numbers of variables: a shorter sumcheck can be padded up to match a longer one.

The sumcheck protocol binds variables in high-index to low-index order, so the n_extra_vars padding variables (the highest-indexed ones) are bound first. Concretely:

• In a padding round i < n_extra_vars, the round polynomial is $R_i(X) = s \cdot \text{eq}(0, X) \cdot \prod_{k<i} \text{eq}(0, r_k)$, where $r_k$ is the $k$-th challenge. This is a genuine degree-1 polynomial built without touching the inner prover. It is emitted with degree + 1 coefficients, the ones above $X^1$ zero, so a batch that contains it has the full degree in every round, even when this prover is the only one of that degree.
• In an inner round i \ge n_extra_vars, the round polynomial is $R^\text{inner}{i - n\text{extra}}(X) \cdot \prod_{k<n_\text{extra}} \text{eq}(0, r_k)$.

The accumulated equality factor $\prod_{k} \text{eq}(0, r_k)$ over the padding challenges is tracked in eq_prefix; it stops changing once the padding rounds are done.

Implementations

impl<F: Field, Inner: SumcheckProver<F>> PaddedSumcheckDecorator<F, Inner>

pub const fn new( inner: Inner, n_extra_vars: usize, claims: Vec<F>, degree: usize, ) -> Self

Wraps inner, padding its claim with n_extra_vars extra (highest-indexed) variables.

Arguments

• inner - The prover whose variable count is being raised.
• n_extra_vars - How many padding variables to prepend.
• claims - The inner prover’s claimed sums, one per claim.
• degree - The round degree the verifier reads, at least 1. The padding rounds are emitted at this degree.

Trait Implementations

impl<F: Clone + Field, Inner: Clone> Clone for PaddedSumcheckDecorator<F, Inner>

fn clone(&self) -> PaddedSumcheckDecorator<F, Inner>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<F: Debug + Field, Inner: Debug> Debug for PaddedSumcheckDecorator<F, Inner>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<F: Field, Inner: SumcheckProver<F>> SumcheckProver<F> for PaddedSumcheckDecorator<F, Inner>

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.