Title: Differential uniformity properties of some classes of permutation polynomials Show Chinese title

Title: 某些排列多项式类的微分均匀性性质

Abstract: The notion of $c$-differential uniformity has recently received a lot of attention since its proposal~\cite{Ellingsen}, and recently a characterization of perfect $c$-nonlinear functions in terms of difference sets in some quasigroups was obtained in~\cite{AMS22}. Independent of their applications as a measure for certain statistical biases, the construction of functions, especially permutations, with low $c$-differential uniformity is an interesting mathematical 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由于其提出~\cite{Ellingsen}而受到广泛关注，并且最近在~\cite{AMS22}中获得了关于某些拟群中完美$c$-非线性函数的差集表征。 作为衡量某些统计偏差的指标，它们的构造，特别是具有低$c$-微分均匀性的函数，尤其是排列，在这个领域是一个有趣的数学问题，最近的工作在此方向上投入了大量精力。 我们提供了几类具有低$c$-微分均匀性的排列多项式。 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，我们认为这些可能有独立的兴趣。