The c-differential Uniformity Of A Class of Permutation Polynomial

Finding functions, particularly permutations, with good differential properties has received a lot of attention due to their possible applications. For instance, in combinatorial design theory, a correspondence of perfect c-nonlinear functions and difference sets in some quasigroups was recently shown [1]. In this paper, we re-investigate the c-differential uniformity of a classes of permutation polynomials [7] by multivariate methods. The result shows that it is easier for our proof by multivariate methods than the one of [7] by Walsh transforms computations, Weil sums, and some detailed investigation of the involved equations via number theory tools. Furthermore, we also extend their theorem.