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Title:
Revisiting the IPA-sumcheck connection
Authors: Liam Eagen, Ariel Gabizon
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.
ePrint: https://eprint.iacr.org/2025/1325
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