The One-Round Functions of the DES Generate the Alternating Group

  • Ralph Wernsdorf
Conference paper

DOI: 10.1007/3-540-47555-9_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 658)
Cite this paper as:
Wernsdorf R. (1993) The One-Round Functions of the DES Generate the Alternating Group. In: Rueppel R.A. (eds) Advances in Cryptology — EUROCRYPT’ 92. EUROCRYPT 1992. Lecture Notes in Computer Science, vol 658. Springer, Berlin, Heidelberg


In each of the 16 DES rounds we have a permutation of 64-bitblocks. According to the corresponding key-block there are 248 possible permutations per round. In this paper we will prove that these permutations generate the alternating group. The main parts of the paper are the proof that the generated group is 3-transitive, and the application of a result from P. J. Cameron based on the classification of finite simple groups. A corollary concerning n-round functions generalizes the result.

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ralph Wernsdorf
    • 1
  1. 1.SIT Gesellschaft für Systeme der Informationstechnik mbHGrünheide (Mark)Germany

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