How to construct universal one-way hash functions of order r

Deukjo Hong, Jaechul Sung, Seokhie Hong, Sangjin Lee

Research output: Chapter in Book/Report/Conference proceedingConference contribution


At ASIACRYPT 2004, Hong et al. introduced the notion of UOWHFs of order r > 0. A UOWHF has the order r if it is infeasible for any adversary to win the game for UOWHF where the adversary is allowed r adaptive queries to the hash function oracle before outputting his target message. They showed that if a UOWHF has the order r, its some-round MD (Merkle-Damgård) or some-level TR (TRee) extension is a UOWHF. Since MD and TR extensions do not require additional key values except the key of compression functions for hashing, their result means that the order of UOWHFs can be useful for minimizing the total key length. In this paper we study how to construct such UOWHFs of order r. As the first step, we observe Bellare-Rogaway UOWHF and Naor-Yung UOWHF. It is shown that Bellare-Rogaway UOWHF has the order 0 and that Naor-Yung UOWHF has the order 1. We generalize the construction of Naor-Yung UOWHF based on a one-way permutation to that of the UOWHF of order r.

Original languageEnglish
Title of host publicationProgress in Cryptology - INDOCRYPT 2005 - 6th International Conference on Cryptology in India, Proceedings
PublisherSpringer Verlag
Number of pages14
ISBN (Print)3540308059, 9783540308058
Publication statusPublished - 2005
Event6th International Conference on Cryptology in India, INDOCRYPT 2005 - Bangalore, India
Duration: 2005 Dec 102005 Dec 12

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3797 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other6th International Conference on Cryptology in India, INDOCRYPT 2005


  • Collision Resistant Hash Function (CRHF)
  • Hash Function
  • Higher Order Universal One-Way Hash Function
  • Universal One-Way Hash Function (UOWHF)

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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