Some highly symmetric authentication perpendicular arrays

✍ Scribed by Jürgen Bierbrauer; Tran Trung

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 541 KB
• Volume: 1
• Category: Article
• ISSN: 0925-1022
• DOI: 10.1007/bf00124606

✦ Synopsis

A set $ of permutations of k objects is ~t-ttmform, t-homogeneous if for every pair A, B of t-subsets of the ground set, there are exactly tt permutations in S mapping A onto B Arithmetical conditions and symmetries are discussed. We describe the character-theoretic method which is useful if S is contained in a permutation group. A main result is the construction of a 2-uniform, 2-homogeneous set of permutations on 6 objects and of a 3-uniform, 3-homogeneous set of permutations on 9 objects. These are contained in the simple permutalion groups PSL~(5) and PSL~(g), respectively. The result is useful in the framework of theoretical secrecy and authentication (see Stinson 1990, Bierbrauer andTran 1991).

using the affine group. We settle the smallest open case by constructing an APA2(2, 6, 6). This APA is contained in the group A s in its action on the projective line tPt(5). Its symmetry group has order 50. We note that this might be considered as a substitute for a