Markov Ciphers and Alternating Groups

  • G. Hornauer
  • W. Stephan
  • R. Wernsdorf
Conference paper

DOI: 10.1007/3-540-48285-7_41

Part of the Lecture Notes in Computer Science book series (LNCS, volume 765)
Cite this paper as:
Hornauer G., Stephan W., Wernsdorf R. (1994) Markov Ciphers and Alternating Groups. In: Helleseth T. (eds) Advances in Cryptology — EUROCRYPT ’93. EUROCRYPT 1993. Lecture Notes in Computer Science, vol 765. Springer, Berlin, Heidelberg

Abstract

This paper includes some relations between differential cryptanalysis and group theory. The main result is the following: If the one-round functions of an r-round iterated cipher generate the alternating or the symmetric group, then for all corresponding Markov ciphers the chains of differences are irreducible and aperiodic.

As an application it will be shown that if the hypothesis of stochastic equivalence holds for any of these corresponding Markov ciphers, then the DES and the IDEA(32) are secure against a differential cryptanalysis attack after sufficiently many rounds for these Markov ciphers.

The section about IDEA(32) includes the result that the one-round functions of this algorithm generate the alternating group.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • G. Hornauer
    • 1
  • W. Stephan
    • 1
  • R. Wernsdorf
    • 1
  1. 1.SIT Gesellschaft für Systeme der Informationstechnik mbHGrünheide (Mark)Germany

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