Permutation generators of alternating groups

  • Josef Pieprzyk
  • Xian-Mo Zhang
Section 6 Block Ciphers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 453)


The problem of generation of permutations from small ones is especially important from a cryptographic point of view. This work explores the case This work addresses the design of cryptographic systems using elementary permutations, also called modules. These modules have a simple structure and are based on internal smaller permutations. Two cases have been considered. In the first, the modules apply internal permutations only. It has been proved that the composition of modules generates the alternating group for the number of binary inputs bigger than 2. In the second, DES-like modules are considered and it has been shown that for a large enough number of binary inputs, they produce the alternating group, as well.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Bovey and A. Williamson. The probability of generating the symmetric group. Bull. London Math. Soc., 10:91–96, 1978.Google Scholar
  2. [2]
    D. Coppersmith and E. Grossman. Generators for certain alternating groups with applications to cryptography. SIAM Journal Appl. Math., 29(4):624–627, December 1975.Google Scholar
  3. [3]
    S. Even and O. Goldreich. DES-like functions can generate the alternating group. IEEE Transaction on Inf. Theory, IT-29(6):863–865, November 1983.Google Scholar
  4. [4]
    Data Encryption Standard. National bureau of standards. Federal Information Processing Standard Publication, January 1977. No.46.Google Scholar
  5. [5]
    H. Wielandt. Finite permutation groups. Academic Press, New York, 1964.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Josef Pieprzyk
    • 1
  • Xian-Mo Zhang
    • 1
  1. 1.Department of Computer Science University CollegeUniversity of New South Wales Australian Defence Force AcademyCanberraAustralia

Personalised recommendations