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International Conference on Information Security

ISC 2003: Information Security pp 280–294Cite as

Foundations of Differential Cryptanalysis in Abelian Groups

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2851))

Abstract

Differential cryptanalysis is based on differentials having relatively high probability. Hawkes and O’Connor studied maximal differential probabilities for three most common operations used as components in ciphers: XOR, modular addition and modular multiplication. They showed that the upper bound for these probabilities for two latter operations is actually a lower bound for maximal probabilities of differentials based on XOR. In this paper we analyse such bounds in abelian groups of odd order and generalize Hawkes and O’Connor’s result. We show that for all operations in these groups the upper bound is the same as for addition mod 2n. This means that no odd order abelian group leads to such high probabilities of differentials as in an abelian group with XOR operation.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland

    Tomasz Tyksiński

Authors
  1. Tomasz Tyksiński
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Editor information

Editors and Affiliations

  1. Information Security Institute, Queensland University of Technology, GPO Box 2434, Qld 4001, Brisbane, Australia

    Colin Boyd

  2. Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, BS34 8QZ, Bristol, UK

    Wenbo Mao

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© 2003 Springer-Verlag Berlin Heidelberg

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Tyksiński, T. (2003). Foundations of Differential Cryptanalysis in Abelian Groups. In: Boyd, C., Mao, W. (eds) Information Security. ISC 2003. Lecture Notes in Computer Science, vol 2851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10958513_22

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  • DOI: https://doi.org/10.1007/10958513_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20176-2

  • Online ISBN: 978-3-540-39981-0

  • eBook Packages: Springer Book Archive

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