Informally, we consider a general notion of bilinear commitment over modules, and show that the sumcheck protocol applied to a certain polynomial associated with the commitment scheme yields a succinct argument of knowledge for openings of the commitment. Building on this, we additionally obtain succinct arguments for the NP-complete language R1CS over certain rings.
Sumcheck arguments enable us to recover as a special case numerous prior works in disparate cryptographic settings (such as discrete logarithms, pairings, groups of unknown order, lattices), providing one abstract framework to understand them all. Further, we answer open questions raised in prior works, such as obtaining a lattice-based succinct argument from the SIS assumption for satisfiability problems over rings.
Category / Keywords: cryptographic protocols / sumcheck protocol; succinct arguments; scalar-product protocol Date: received 14 Mar 2021 Contact author: jbt at zurich ibm com, alexch@berkeley edu, katesot@berkeley edu Available format(s): PDF | BibTeX Citation Note: In submission. Version: 20210314:150810 (All versions of this report) Short URL: ia.cr/2021/333