Expand description
Interactive reduction from evaluation claims on committed small-field multilinear polynomials to sumcheck claims on products of committed packed multilinears and transparent polynomials.
This is a batched version of the ring-switching reduction from section 4 of DP24. The plain, non-batched ring-switching interactive reduction reduces an evaluation claim on a multilinear to a sumcheck on a composition of its corresponding packed polynomial.
The input claim for a multilinear $f(X_0, …, X_{\ell-1})$ is
$$ f(z_0, …, z_{\ell-1}) = s. $$
The multilinear $t$ has a corresponding “packed” multilinear $t’$, with $\kappa$ fewer variables. Ring-switching reduces the input claim to a sumcheck claim that
$$ \sum_{v \in B_{\ell’}} f’(v) t_z(v) = s’. $$
TODO: Improve documentation and link to binius.xyz docs.
Structs§
- Eval
Claim Prefix Desc - A prefix of an evaluation claim query.
- Eval
Claim Suffix Desc - A suffix of an evaluation claim query.
- Eval
Claim System - A system of relations required to verify multilinear evaluation claims using the batched FRI-Binius protocol.
- PIOP
Sumcheck Claim Desc - An incomplete
crate::piop::PIOPSumcheckClaimfor which the sum has not been determined yet. - Reduced
Claim - Reduced
Witness