Work

A divide-and-conquer sumcheck protocol

Year: 2025

Type: article

Abstract: We present a new sumcheck protocol called Fold-DCS (Fold-Divide-and-Conquer-Sumcheck) for multivariate polynomials based on a divide-and-conquer strategy. Its round complexity and soundness error are logarithmic in the number of variables, whereas they are linear in the classical sumcheck protocol. This drastic improvement in number of rounds and soundness comes at the expense of exchanging multivariate polynomials, which can be alleviated using polynomial commitment schemes. We first present Fold-DCS in the PIOP model, where the prover provides oracle access to a multivariate polynomial at each round. We then replace this oracle access in practice with a multivariate polynomial commitment scheme; we illustrate this with an adapted version of the recent commitment scheme Zeromorph, which allows us to replace most of the queries made by the verifier with a single batched evaluation check.

Source: IACR Communications in Cryptology

DOI: 10.62056/abksdk5vt

Authors: Christophe Levrat, Tanguy Medevielle, Jade Nardi

Institutions: Institut national de recherche en sciences et technologies du numérique, Centre Inria de Saclay, Centre National de la Recherche Scientifique, Institut de recherche mathématique de Rennes, Université de Rennes

Language: English

Topic: Cryptography and Data Security

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: Agence Nationale de la Recherche

Awards: algeBrA, pRoofs, Algorithms, Curves and sUrfaces for coDes and their Applications, Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation