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Birthday Paradox for Multi-collisions

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Information Security and Cryptology – ICISC 2006 (ICISC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4296))

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Abstract

In this paper, we study multi-collision probability. For a hash function H:D →R with |R|=n, it has been believed that we can find an s-collision by hashing Q=n ( s − − 1)/ s times. We first show that this probability is at most 1/s! which is very small for large s. We next show that by hashing (s!)1/ s ×Q times, an s-collision is found with probability approximately 0.5 for sufficiently large n. Note that if s=2, it coincides with the usual birthday paradox. Hence it is a generalization of the birthday paradox to multi-collisions.

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Authors and Affiliations

  1. Venture Business Laboratory, Ibaraki University, 4–12–1 Nakanarusawa, Hitachi, Ibaraki, 316-8511, Japan

    Kazuhiro Suzuki

  2. School of Information Technology and Computer Science, University of Wollongong, Wollongong, 2522, Australia

    Dongvu Tonien

  3. Department of Computer and Information Sciences, Ibaraki University, 4–12–1 Nakanarusawa, Hitachi, Ibaraki, 316-8511, Japan

    Kaoru Kurosawa & Koji Toyota

Authors
  1. Kazuhiro Suzuki
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  2. Dongvu Tonien
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  3. Kaoru Kurosawa
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  4. Koji Toyota
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Editor information

Editors and Affiliations

  1. Dankook University, San 29, Anseo-dong, Cheonan-shi, 330-714, Chungnam, Korea

    Min Surp Rhee

  2. Department of Information Security, Joongbu University, 101 Daehak-Ro, Chubu-Myeon, Geumsan-Gun,, 312-702, Chungnam, Korea

    Byoungcheon Lee

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© 2006 Springer-Verlag Berlin Heidelberg

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Suzuki, K., Tonien, D., Kurosawa, K., Toyota, K. (2006). Birthday Paradox for Multi-collisions. In: Rhee, M.S., Lee, B. (eds) Information Security and Cryptology – ICISC 2006. ICISC 2006. Lecture Notes in Computer Science, vol 4296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11927587_5

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  • DOI: https://doi.org/10.1007/11927587_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49112-5

  • Online ISBN: 978-3-540-49114-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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