Title: Several classes of permutation polynomials and their differential uniformity properties Show Chinese title

Title: 一些排列多项式的类及其差分均匀性性质

Abstract: The notion of $c$-differential uniformity has recently received a lot of popularity because of its potential applications in cryptography (we point out that a connection with difference sets in some quasigroups is already realized for perfect $c$-nonlinear functions, in a recent manuscript~\cite{AMS22}). The construction of functions, especially permutations, with low $c$-differential uniformity is an interesting problem in this area, and recent work has focused heavily in this direction. We provide a few classes of permutation polynomials with low $c$-differential uniformity. The used technique involves handling various Weil sums, as well as analyzing some equations in finite fields, and we believe these can be of independent interest. Show Chinese abstract

Abstract: $c$-微分均匀性的概念最近受到了广泛关注，因为它在密码学中的潜在应用（我们指出，在最近的一篇手稿~\cite{AMS22}中已经实现了与某些拟群中差集的联系，针对完美$c$-非线性函数）。 构造具有低$c$-微分均匀性的函数，特别是置换函数，是这一领域的一个有趣问题，近期的研究主要集中在这一方向。 我们提供了一些具有低$c$-微分均匀性的置换多项式类。 所使用的技术涉及处理各种Weil和，以及分析有限域中的一些方程，我们认为这些可能具有独立的兴趣。