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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti

CiteScore 2018: 1.41

SCImago Journal Rank (SJR) 2018: 0.342
Source Normalized Impact per Paper (SNIP) 2018: 1.076

Mathematical Citation Quotient (MCQ) 2017: 0.51

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Volume 4, Issue 2


The power of primes: security of authentication based on a universal hash-function family

Basel Alomair
  • Center of Excellence in Information Assurance (CoEIA), King Saud University, Riyadh, Saudi Arabia, and Network Security Lab (NSL), University of Washington, Seattle, USA. E-mail:
  • Other articles by this author:
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/ Andrew Clark / Radha Poovendran
Published Online: 2010-07-21 | DOI: https://doi.org/10.1515/jmc.2010.005


Message authentication codes (MACs) based on universal hash-function families are becoming increasingly popular due to their fast implementation. In this paper, we investigate a family of universal hash functions that has been appeared repeatedly in the literature and provide a detailed algebraic analysis for the security of authentication codes based on this universal hash family. In particular, the universal hash family under analysis, as appeared in the literature, uses operation in the finite field ℤp. No previous work has studied the extension of such universal hash family when computations are performed modulo a non-prime integer n. In this work, we provide the first such analysis. We investigate the security of authentication when computations are performed over arbitrary finite integer rings ℤn and derive an explicit relation between the prime factorization of n and the bound on the probability of successful forgery. More specifically, we show that the probability of successful forgery against authentication codes based on such a universal hash-function family is bounded by the reciprocal of the smallest prime factor of the modulus n.

Keywords.: Cryptography; authentication; finite integer rings; universal hash-function families

About the article

Received: 2009-10-08

Revised: 2010-04-05

Published Online: 2010-07-21

Published in Print: 2010-10-01

Citation Information: Journal of Mathematical Cryptology, Volume 4, Issue 2, Pages 121–148, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc.2010.005.

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