The c-differential Uniformity Of A Class of Permutation Polynomial

Key Points

The result indicates easier proof for c-differential uniformity using multivariate methods, highlighting efficiency.
Key evidence shows that previously complex approaches involving Walsh transforms were less effective.
This analysis utilized multivariate methods to reassess c-differential uniformity in a class of permutation polynomials.
Findings suggest potential improvements in combinatorial design theory by applying simpler proof techniques.

Abstract

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.

The c-differential Uniformity Of A Class of Permutation Polynomial

Key Points

Abstract

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