From obfuscation to the security of fiat-shamir for proofs

Yael Tauman Kalai, Guy N. Rothblum, Ron D. Rothblum

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

Abstract

The Fiat-Shamir paradigm [CRYPTO’86] is a heuristic for converting three-round identification schemes into signature schemes, and more generally, for collapsing rounds in constant-round public-coin interactive protocols. This heuristic is very popular both in theory and in practice, and its security has been the focus of extensive study. In particular, this paradigm was shown to be secure in the Random Oracle Model. However, in the plain model, the results shown were mostly negative. In particular, the heuristic was shown to be insecure when applied to computationally sound proofs (also known as arguments). Moreover, recently it was shown that even in the restricted setting where the heuristic is applied to interactive proofs (as opposed to arguments), its soundness cannot be proven via a black-box reduction to any so-called falsifiable assumption. In this work, we give a positive result for the security of this paradigm in the plain model. Specifically, we construct a hash function for which the Fiat Shamir paradigm is secure when applied to proofs (as opposed to arguments), assuming the existence of a sub-exponentially secure indistinguishability obfuscator, the existence of an exponentially secure input-hiding obfuscator for the class of multi-bit point functions, and the existence of a sub-exponentially secure one-way function. More generally, we construct a hash family that is correlation intractable (under the computational assumptions above), solving an open problem originally posed by Canetti, Goldreich and Halevi (JACM, 2004), under the above assumptions. In addition, we show that our result resolves a long-lasting open problem in about zero-knowledge proofs: It implies that there does not exist a public-coin constant-round zero-knowledge proof with negligible soundness (under the assumptions stated above).

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2017
Subtitle of host publication37th Annual International Cryptology Conference, Proceedings
EditorsJonathan Katz, Hovav Shacham
PublisherSpringer Verlag
Pages224-251
Number of pages28
ISBN (Print)9783319637143
DOIs
StatePublished - 29 Jul 2017
Event37th Annual International Cryptology Conference, CRYPTO 2017 - Santa Barbara, United States
Duration: 20 Aug 201724 Aug 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10402 LNCS

Conference

Conference37th Annual International Cryptology Conference, CRYPTO 2017
Country/TerritoryUnited States
CitySanta Barbara
Period20/08/1724/08/17

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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