On distributional collision resistant hashing

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

Abstract

Collision resistant hashing is a fundamental concept that is the basis for many of the important cryptographic primitives and protocols. Collision resistant hashing is a family of compressing functions such that no efficient adversary can find any collision given a random function in the family. In this work we study a relaxation of collision resistance called distributional collision resistance, introduced by Dubrov and Ishai (STOC ’06). This relaxation of collision resistance only guarantees that no efficient adversary, given a random function in the family, can sample a pair (x, y) where x is uniformly random and y is uniformly random conditioned on colliding with x. Our first result shows that distributional collision resistance can be based on the existence of multi-collision resistance hash (with no additional assumptions). Multi-collision resistance is another relaxation of collision resistance which guarantees that an efficient adversary cannot find any tuple of (formula presented) inputs that collide relative to a random function in the family. The construction is non-explicit, non-black-box, and yields an infinitely-often secure family. This partially resolves a question of Berman et al. (EUROCRYPT ’18). We further observe that in a black-box model such an implication (from multi-collision resistance to distributional collision resistance) does not exist. Our second result is a construction of a distributional collision resistant hash from the average-case hardness of SZK. Previously, this assumption was not known to imply any form of collision resistance (other than the ones implied by one-way functions).

Original languageAmerican English
Title of host publicationAdvances in Cryptology – CRYPTO 2018 - 38th Annual International Cryptology Conference, 2018, Proceedings
EditorsAlexandra Boldyreva, Hovav Shacham
PublisherSpringer Verlag
Pages303-327
Number of pages25
ISBN (Print)9783319968803
DOIs
StatePublished - Jul 2018
Event38th Annual International Cryptology Conference, CRYPTO 2018 - Santa Barbara, United States
Duration: 19 Aug 201823 Aug 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10992 LNCS

Conference

Conference38th Annual International Cryptology Conference, CRYPTO 2018
Country/TerritoryUnited States
CitySanta Barbara
Period19/08/1823/08/18

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

Fingerprint

Dive into the research topics of 'On distributional collision resistant hashing'. Together they form a unique fingerprint.

Cite this