On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations

Nir Bitansky*, Akshay Degwekar

*Corresponding author for this work

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

8 Scopus citations


The complexity of collision-resistant hash functions has been long studied in the theory of cryptography. While we often think about them as a Minicrypt primitive, black-box separations demonstrate that constructions from one-way functions are unlikely. Indeed, theoretical constructions of collision-resistant hash functions are based on rather structured assumptions. We make two contributions to this study: 1.A New Separation: We show that collision-resistant hashing does not imply hard problems in the class Statistical Zero Knowledge in a black-box way.2.New Proofs: We show new proofs for the results of Simon, ruling out black-box reductions of collision-resistant hashing to one-way permutations, and of Asharov and Segev, ruling out black-box reductions to indistinguishability obfuscation. The new proofs are quite different from the previous ones and are based on simple coupling arguments.

Original languageEnglish
Title of host publicationTheory of Cryptography - 17th International Conference, TCC 2019, Proceedings
EditorsDennis Hofheinz, Alon Rosen
Number of pages29
ISBN (Print)9783030360290
StatePublished - 2019
Event17th International Conference on Theory of Cryptography, TCC 2019 - Nuremberg, Germany
Duration: 1 Dec 20195 Dec 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11891 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Conference on Theory of Cryptography, TCC 2019


FundersFunder number
Alon Young Faculty Fellowship
U.S. Army Research OfficeW911NF-15-C-0236, W911NF-15-C-0226
National Science FoundationCNS-1413920, CNS-1350619
Air Force Office of Scientific ResearchFA9550-17-1-0069
Defense Advanced Research Projects Agency
Blavatnik Family Foundation
Israel Science Foundation18/484, 1861/16


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