Collision resistant hashing for paranoids: dealing with multiple collisions

Ilan Komargodski*, Moni Naor, Eylon Yogev

*Corresponding author for this work

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

24 Scopus citations

Abstract

A collision resistant hash (CRH) function is one that compresses its input, yet it is hard to find a collision, i.e. a x1≠ x2 s.t. h(x1) = h(x2). Collision resistant hash functions are one of the more useful cryptographic primitives both in theory and in practice and two prominent applications are in signature schemes and succinct zero-knowledge arguments. In this work we consider a relaxation of the above requirement that we call Multi-CRH: a function where it is hard to find x1, x2, …, xk which are all distinct, yet h(x1) = h(x2) = ⋯ = h(xk). We show that for some of the major applications of CRH functions it is possible to replace them by the weaker notion of a Multi-CRH, albeit at the price of adding interaction: we show a constant-round statistically-hiding commitment scheme with succinct interaction (committing to poly(n) bits requires exchanging O~ (n) bits) that can be opened locally (without revealing the full string). This in turn can be used to provide succinct arguments for any NP statement. We formulate four possible worlds of hashing-related assumptions (in the spirit of Impagliazzo’s worlds). They are (1) Nocrypt, where no one-way functions exist, (2) Unihash, where one-way functions exist, and hence also UOWHFs and signature schemes, but no Multi-CRH functions exist, (3) Minihash, where Multi-CRH functions exist but no CRH functions exist, and (4) Hashomania, where CRH functions exist. We show that these four worlds are distinct in a black-box model: we show a separation of CRH from Multi-CRH and a separation of Multi-CRH from one-way functions.

Original languageAmerican English
Title of host publicationAdvances in Cryptology - EUROCRYPT 2018 - 37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2018 Proceedings
EditorsJesper Buus Nielsen, Vincent Rijmen
PublisherSpringer Verlag
Pages162-194
Number of pages33
ISBN (Print)9783319783741
DOIs
StatePublished - 2018
Externally publishedYes
Event37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2018 - Tel Aviv, Israel
Duration: 29 Apr 20183 May 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10821 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference37th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2018
Country/TerritoryIsrael
CityTel Aviv
Period29/04/183/05/18

Bibliographical note

Publisher Copyright:
© 2018, International Association for Cryptologic Research.

Fingerprint

Dive into the research topics of 'Collision resistant hashing for paranoids: dealing with multiple collisions'. Together they form a unique fingerprint.

Cite this