International Association
for Cryptologic Research

In this paper we consider permutations on n symbols as bijections

on Z/nZ. Treating permutations this way facilitates us with additional

structures such as group, ring defined in the set Z/nZ. We explore

some of the properties of permutations arising out of this treatment.

We propose two properties viz. affine equivalence and non-linearity for permutations on the lines similar to there description given in the case of functions. We also establish some results which are quite similar to those given for Boolean functions. We also define Mode Transform of a permutation and investigate its relationship with non-linearity.

We propose an efficient algorithm using Mode transform for computing non-linearity of a permutation and show that it is O(n^2), as

compared to O(n^3) of the direct approach. At the end we discuss

these properties in the context of cryptography.