Lower Bound on SNARGs in the Random Oracle Model

Iftach Haitner, Daniel Nukrai, Eylon Yogev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Succinct non-interactive arguments (SNARGs) have become a fundamental primitive in the cryptographic community. The focus of this work is constructions of SNARGs in the Random Oracle Model (ROM). Such SNARGs enjoy post-quantum security and can be deployed using lightweight cryptography to heuristically instantiate the random oracle. A ROM-SNARG is (t, ε) -sound if no t -query malicious prover can convince the verifier to accept a false statement with probability larger than ε. Recently, Chiesa-Yogev (CRYPTO ’21) presented a ROM-SNARG of length Θ(log (t/ ε) · log t) (ignoring log n factors, for n being the instance size). This improvement, however, is still far from the (folklore) lower bound of Ω(log (t/ ε) ). Assuming the randomized exponential-time hypothesis, we prove a tight lower bound of Ω(log (t/ ε) · log t) for the length of (t, ε) -sound ROM-SNARGs. Our lower bound holds for constructions with non-adaptive verifiers and strong soundness notion called salted soundness, restrictions that hold for all known constructions (ignoring contrived counterexamples). We prove our lower bound by transforming any short ROM-SNARG (of the considered family) into a same length ROM-SNARG in which the verifier asks only a few oracles queries, and then apply the recent lower bound of Chiesa-Yogev (TCC ’20) for such SNARGs.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2022 - 42nd Annual International Cryptology Conference, CRYPTO 2022, Proceedings
EditorsYevgeniy Dodis, Thomas Shrimpton
PublisherSpringer Science and Business Media Deutschland GmbH
Pages97-127
Number of pages31
ISBN (Print)9783031159817
DOIs
StatePublished - 2022
Event42nd Annual International Cryptology Conference, CRYPTO 2022 - Santa Barbara, United States
Duration: 15 Aug 202218 Aug 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13509 LNCS

Conference

Conference42nd Annual International Cryptology Conference, CRYPTO 2022
Country/TerritoryUnited States
CitySanta Barbara
Period15/08/2218/08/22

Keywords

  • Random oracle
  • SNARGs
  • high-entropy sets
  • lower bound

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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