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.

翻译：$c$-微分均匀性的概念自提出以来~\cite{Ellingsen}便受到了广泛关注，近期文献~\cite{AMS22}通过拟群中的差集刻画了完美$c$-非线性函数。独立于其作为特定统计偏差度量的应用，构造具有低$c$-微分均匀性的函数（尤其是置换函数）是该领域中一项有趣的数学问题，近期研究主要集中于此方向。本文提供了若干类具有低$c$-微分均匀性的置换多项式。所采用的技术涉及处理各类Weil和以及分析有限域中的方程，我们相信这些方法本身亦具有独立的研究价值。