Some highly symmetric authentication perpendicular arrays

Abstract

A set S of permutations of k objects is μ-uniform, t-homogeneous if for every pair A, B of t-subsets of the ground set, there are exactly μ 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 permutation groups PSL2(5) and PSL2(8), respectively. The result is useful in the framework of theoretical secrecy and authentication (see Stinson 1990, Bierbrauer and Tran 1991).