Differential -uniformity and non-linearity of permutations over Zn.

Differential uniformity and non-linearity of functions are the properties of great interest in cryptographic world. In this article, both the properties have been explored when the function is a permutation over Zn and some interesting results have been obtained. Also, some differential n-uniform non-affine permutations have been constructed over Zn, n being composite. Inversion permutation over GF(2n) is known to have good non-linearity and differential uniformity. Its behaviour with respect to these properties has been studied over another domain, the ring of integer modulo p, where p is a prime. Further, conditions for maximum possible value of differential uniformity and non-linearity have been derived for permutations obtained by swapping two positions in the inversion permutation.