Paper 2025/1325

Revisiting the IPA-sumcheck connection

Abstract

Inner Product Arguments (IPA) [BCC+16,BBB+17] are a family of proof systems with $O(\log n)$ sized proofs, $O(n)$ time verifiers, and transparent setup. Bootle, Chiesa and Sotiraki [BCS21] observed that an IPA can be viewed as a sumcheck protocol [LFKN92] where the summed polynomial is allowed to have coefficients in a group rather than a field. We leverage this viewpoint to improve the performance of multi-linear polynomial commitments based on IPA. Specifically, - We introduce a simplified variant of Halo-style accumulation that works for multilinear evaluation claims, rather than only univariate ones as in [BGH19,BCMS20]. - We show that the size $n$ MSM the IPA verifier performs can be replaced by a ``group variant'' of $\mathsf{basefold}$[ZCF23]. This reduces the verifier complexity from $O(n)$ to $O_{\lambda}(\log^2 n)$ time at the expense of an additional $4n$ scalar multiplications for the IPA prover.

Note: Fix reduce protocol to randomize generator P