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Designs, Codes and Cryptography

, Volume 9, Issue 1, pp 29–38 | Cite as

Some t-Homogeneous Sets of Permutations

  • Jürgen Bierbrauer
  • Stephen Black
  • Yves Edel
Article

Abstract

Perpendicular Arrays are orderedcombinatorial structures, which recently have found applicationsin cryptography. A fundamental construction uses as ingredientscombinatorial designs and uniformly t-homogeneoussets of permutations. We study the latter type of objects. Thesemay also be viewed as generalizations of t-homogeneousgroups of permutations. Several construction techniques are given.Here we concentrate on the optimal case, where the number ofpermutations attains the lower bound. We obtain several new optimalsuch sets of permutations. Each example allows the constructionof infinite families of perpendicular arrays.

Permutation sets permutation groups perpendicular arrays authentication 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Jürgen Bierbrauer
    • 1
  • Stephen Black
    • 2
  • Yves Edel
    • 3
  1. 1.Department of Mathematical SciencesMichigan Technological UniversityHoughtonUSA
  2. 2.IBM Heidelberg (Germany) Mathematisches Institut der UniversitätHeidelberg (Germany
  3. 3.Mathematisches Institut der UniversitätHeidelberg (Germany

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