Collision-Resistance from Multi-Collision-Resistance

Ron D. Rothblum, Prashant Nalini Vasudevan

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

Abstract

Collision-resistant hash functions (CRH ) are a fundamental and ubiquitous cryptographic primitive. Several recent works have studied a relaxation of CRH called t-way multi-collision-resistant hash functions (t- MCRH ). These are families of functions for which it is computationally hard to find a t-way collision, even though such collisions are abundant (and even (t- 1 ) -way collisions may be easy to find). The case of t= 2 corresponds to standard CRH, but it is natural to study t- MCRH for larger values of t. Multi-collision-resistance seems to be a qualitatively weaker property than standard collision-resistance. Nevertheless, in this work we show a non-blackbox transformation of any moderately shrinking t- MCRH, for t∈ { 3, 4 }, into an (infinitely often secure) CRH. This transformation is non-constructive – we can prove the existence of a CRH but cannot explicitly point out a construction. Our result partially extends to larger values of t. In particular, we show that for suitable values of t> t, we can transform a t- MCRH into a t - MCRH, at the cost of reducing the shrinkage of the resulting hash function family and settling for infinitely often security. This result utilizes the list-decodability properties of Reed-Solomon codes.

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
Pages503-529
Number of pages27
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

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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