论文标题
某些类别的置换多项式的差异均匀性能
Differential uniformity properties of some classes of permutation polynomials
论文作者
论文摘要
自提议〜\ cite {ellingsen}以来，$ c $ - 差异均匀性的概念最近受到了很多关注，最近在〜\ cite {ams22}中获得了某些quasigroups中的差异集的完美$ c $ -nonlinelear函数的特征。独立于其应用程序作为某些统计偏见的衡量标准，构建功能，尤其是置换率较低的功能，$ c $差异的均匀性是一个有趣的数学问题，并且最近的工作重点朝着这个方向上。我们提供几类置换多项式，具有低$ C $不同的均匀性。使用的技术涉及处理各种Weil总和，并分析有限领域的某些方程式，我们认为这些方程可能具有独立的兴趣。
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.
