Parallel hashing via list recoverability

Iftach Haitner, Yuval Ishai, Eran Omri, Ronen Shaltiel

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

Abstract

Motivated by the goal of constructing efficient hash functions, we investigate the possibility of hashing a long message by only making parallel, non-adaptive calls to a hash function on short messages. Our main result is a simple construction of a collision-resistant hash function h: {0, 1}n → {0, 1}k that makes a polynomial number of parallel calls to a random function f: {0, 1}k → {0, 1}k, for any polynomial n = n(k). This should be compared with the traditional use of a Merkle hash tree, that requires at least log(n/k) rounds of calls to f, and with a more complex construction of Maurer and Tessaro [26] (Crypto 2007) that requires two rounds of calls to f. We also show that our hash function h satisfies a relaxed form of the notion of indifferentiability of Maurer et al. [27] (TCC 2004) that suffices for implementing the Fiat-Shamir paradigm. As a corollary, we get sublinear-communication non-interactive arguments for NP that only make two rounds of calls to a small random oracle. An attractive feature of our construction is that h can be implemented by Boolean circuits that only contain parity gates in addition to the parallel calls to f. Thus, we get the first domain-extension scheme which is degree-preserving in the sense that the algebraic degree of h over the binary field is equal to that of f. Our construction makes use of list-recoverable codes, a generalization of list-decodable codes that is closely related to the notion of randomness condensers. We show that list-recoverable codes are necessary for any construction of this type.

Original languageEnglish
Title of host publicationAdvances in Cryptology - CRYPTO 2015 - 35th Annual Cryptology Conference, Proceedings
EditorsMatthew Robshaw, Rosario Gennaro
PublisherSpringer Verlag
Pages173-190
Number of pages18
ISBN (Print)9783662479995
DOIs
StatePublished - 2015
Event35th Annual Cryptology Conference, CRYPTO 2015 - Santa Barbara, United States
Duration: 16 Aug 201520 Aug 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9216
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference35th Annual Cryptology Conference, CRYPTO 2015
Country/TerritoryUnited States
CitySanta Barbara
Period16/08/1520/08/15

Bibliographical note

Funding Information:
The first author was supported by ISF grant 1076/11, I-CORE grant 4/11, BSF grant 2010196, and Check Point Institute for Information Security. The second author was supported by ERC starting grant 259426, ISF grant 1709/14, and BSF grant 2012378. The third author was supported by ERC starting grants 259426 and 279559, and by ISF grant 544/13. The fourth author was supported by ERC starting grant 279559, BSF grant 2010120, and ISF grant 864/11.

Publisher Copyright:
© International Association for Cryptologic Research 2015.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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