Higher order universal one-way hash functions from the subset sum assumption

Ron Steinfeld*, Josef Pieprzyk, Huaxiong Wang

*Corresponding author for this work

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

Abstract

Universal One-Way Hash Functions (UOWHFs) may be used in place of collision-resistant functions in many public-key cryptographic applications. At Asiacrypt 2004, Hong, Preneel and Lee introduced the stronger security notion of higher order UOWHFs to allow construction of long-input UOWHFs using the Merkle-Damgård domain extender. However, they did not provide any provably secure constructions for higher order UOWHFs. We show that the subset sum hash function is a kth order Universal One-Way Hash Function (hashing n bits to m < n bits) under the Subset Sum assumption for k = O(log n). Therefore we strengthen a previous result of Impagliazzo and Naor, who showed that the subset sum hash function is a UOWHF under the Subset Sum assumption. We believe our result is of theoretical interest; as far as we are aware, it is the first example of a natural and computationally efficient UOWHF which is also a provably secure higher order UOWHF under the same well-known cryptographic assumption, whereas this assumption does not seem sufficient to prove its collision-resistance. A consequence of our result is that one can apply the Merkle-Damgård extender to the subset sum compression function with 'extension factor' k + 1, while losing (at most) about k bits of UOWHF security relative to the UOWHF security of the compression function. The method also leads to a saving of up to m log(k + 1) bits in key length relative to the Shoup XOR-Mask domain extender applied to the subset sum compression function.

Original languageEnglish
Title of host publicationPublic Key Cryptography - PKC 2006 - 9th International Conference on Theory and Practice in Public-Key Cryptography, Proceedings
EditorsMoti Yung, Yevgeniy Dodis, Aggelos Kiayias, Tal Malkin
Place of PublicationBerlin ; New York
PublisherSpringer, Springer Nature
Pages157-173
Number of pages17
Volume3958 LNCS
ISBN (Print)3540338519, 9783540338512
DOIs
Publication statusPublished - 2006
Event9th International Conference on Theory and Practice in Public-Key Cryptography, PKC 2006 - New York, NY, United States
Duration: 24 Apr 200626 Apr 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3958 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other9th International Conference on Theory and Practice in Public-Key Cryptography, PKC 2006
CountryUnited States
CityNew York, NY
Period24/04/0626/04/06

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