From Polynomial IOP and Commitments to Non-malleable zkSNARKs

Antonio Faonio; Dario Fiore; Markulf Kohlweiss; Luigi Russo; Michal Zajac

Paper 2023/569

From Polynomial IOP and Commitments to Non-malleable zkSNARKs

Antonio Faonio

, EURECOM

Dario Fiore

, IMDEA Software

Markulf Kohlweiss

, University of Edinburgh

Luigi Russo

, EURECOM

Michal Zajac, Nethermind

Abstract

We study sufficient conditions for compiling simulation-extractable zkSNARKs from information-theoretic interactive oracle proofs (IOP) using a simulation-extractable commit-and-prove system for its oracles. Specifically, we define simulation extractability for opening and evaluation proofs of polynomial commitment schemes, which we then employ to prove the security of zkSNARKS obtained from polynomial IOP prove systems, such as Plonk and Marlin. To instantiate our methodology we additionally prove that KZG commitments satisfy our simulation extractability requirement, despite being naturally malleable. To this end, we design a relaxed notion of simulation extractability that matches how KZG commitments are used and optimized in real-world prove systems. Only the proof that KZG satisfies this relaxed simulation extractability property relies on the algebraic group model (AGM) and random oracle (RO). We thus isolate the use of (and thus the reliance on) these strong heuristics.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: A major revision of an IACR publication in TCC 2023
Keywords: polynomial commitments non-malleability simulation-extractability zero-knowledge commit-and-prove IOP
Contact author(s): antonio faonio @ eurecom fr
dario fiore @ imdea org
markulf kohlweiss @ ed ac uk
russol @ eurecom fr
michal @ nethermind io
History: 2023-10-09: revised; 2023-04-22: received; See all versions
Short URL: https://ia.cr/2023/569
License: CC BY

BibTeX

@misc{cryptoeprint:2023/569,
      author = {Antonio Faonio and Dario Fiore and Markulf Kohlweiss and Luigi Russo and Michal Zajac},
      title = {From Polynomial IOP and Commitments to Non-malleable zkSNARKs},
      howpublished = {Cryptology ePrint Archive, Paper 2023/569},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/569}},
      url = {https://eprint.iacr.org/2023/569}
}