Universal one-way hash functions via inaccessible entropy

Iftach Haitner, Thomas Holenstein, Omer Reingold, Salil Vadhan, Hoeteck Wee

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

Abstract

This paper revisits the construction of Universal One-Way Hash Functions (UOWHFs) from any one-way function due to Rompel (STOC 1990). We give a simpler construction of UOWHFs, which also obtains better efficiency and security. The construction exploits a strong connection to the recently introduced notion of inaccessible entropy (Haitner et al. STOC 2009). With this perspective, we observe that a small tweak of any one-way function f is already a weak form of a UOWHF: Consider F(x,i) that outputs the i-bit long prefix of f(x). If F were a UOWHF then given a random x and i it would be hard to come up with x′ ≠ x such that F(x,i) = F(x′,i). While this may not be the case, we show (rather easily) that it is hard to sample x′ with almost full entropy among all the possible such values of x′. The rest of our construction simply amplifies and exploits this basic property. With this and other recent works, we have that the constructions of three fundamental cryptographic primitives (Pseudorandom Generators, Statistically Hiding Commitments and UOWHFs) out of one-way functions are to a large extent unified. In particular, all three constructions rely on and manipulate computational notions of entropy in similar ways. Pseudorandom Generators rely on the well-established notion of pseudoentropy, whereas Statistically Hiding Commitments and UOWHFs rely on the newer notion of inaccessible entropy.

Original languageEnglish
Title of host publicationAdvances in Cryptology - Eurocrypt 2010, 29th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Pages616-637
Number of pages22
DOIs
StatePublished - 2010
Externally publishedYes
Event29th in the Series of EuropeanConferences on the Theory and Application of Cryptographic Techniques, Eurocrypt 2010 - French Riviera, France
Duration: 30 May 20103 Jun 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6110 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference29th in the Series of EuropeanConferences on the Theory and Application of Cryptographic Techniques, Eurocrypt 2010
Country/TerritoryFrance
CityFrench Riviera
Period30/05/103/06/10

Keywords

  • computational complexity
  • cryptography
  • hashing
  • one-way functions
  • target collision-resistance

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