Why "Fiat-Shamir for proofs" lacks a proof

Nir Bitansky, Dana Dachman-Soled, Sanjam Garg, Abhishek Jain, Yael Tauman Kalai, Adriana López-Alt, Daniel Wichs

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

Abstract

The Fiat-Shamir heuristic [CRYPTO '86] is used to convert any 3-message public-coin proof or argument system into a non-interactive argument, by hashing the prover's first message to select the verifier's challenge. It is known that this heuristic is sound when the hash function is modeled as a random oracle. On the other hand, the surprising result of Goldwasser and Kalai [FOCS '03] shows that there exists a computationally sound argument on which the Fiat-Shamir heuristic is never sound, when instantiated with any actual efficient hash function. This leaves us with the following interesting possibility: perhaps we can securely instantiates the Fiat-Shamir heuristic for all 3-message public-coin statistically sound proofs, even if we must fail for some computationally sound arguments. Indeed, this has been conjectured to be the case by Barak, Lindell and Vadhan [FOCS '03], but we do not have any provably secure instantiation under any "standard assumption". In this work, we give a broad black-box separation result showing that the security of the Fiat-Shamir heuristic for statistically sound proofs cannot be proved under virtually any standard assumption via a black-box reduction. More precisely: -If we want to have a "universal" instantiation of the Fiat-Shamir heuristic that works for all 3-message public-coin proofs, then we cannot prove its security via a black-box reduction from any assumption that has the format of a "cryptographic game". -For many concrete proof systems, if we want to have a "specific" instantiation of the Fiat-Shamir heuristic for that proof system, then we cannot prove its security via a black box reduction from any "falsifiable assumption" that has the format of a cryptographic game with an efficient challenger.

Original languageEnglish
Title of host publicationTheory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings
Pages182-201
Number of pages20
DOIs
StatePublished - 2013
Event10th Theory of Cryptography Conference, TCC 2013 - Tokyo, Japan
Duration: 3 Mar 20136 Mar 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7785 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th Theory of Cryptography Conference, TCC 2013
Country/TerritoryJapan
CityTokyo
Period3/03/136/03/13

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