Markov ciphers and alternating groups

Authors:
G. Hornauer;R. Wernsdorf;W. Stephan
Affiliations:
SIT Gesellschaft fu¨r Systeme der Informationstechnik mbH, Gru¨nheide, Germany;SIT Gesellschaft fu¨r Systeme der Informationstechnik mbH, Gru¨nheide, Germany;-
Venue:
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Year:
1994

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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.