有限域上的几类PcN幂函数
Several classes of PcN power functions over finite fields
摘要：
最近，Ellingsen等人提出了乘性差分密码分析的概念，并给出了相应的$c$-差分一致性。\cite{Ellingsen2020}，然后构造了一些低微分均匀性函数。本文进一步研究了完全$c$-非线性（PcN）幂函数的构造.首先给出了Gold函数为PcN的一个充要条件和关于$\gf(2^m)$上所有幂函数为PcN的一个猜想。其次，在奇特征有限域上得到了$c=-1$的几类PcN幂函数，推广了\cite{Bartoli,Hasan,Zha2020}中的一些结果.最后，确定了一类几乎完全$c$-非线性（APcN）幂函数的$c$-微分谱.
英文摘要：
Recently, a new concept called multiplicative differential cryptanalysis and the corresponding $c$-differential uniformity were introduced by Ellingsen et al.~\cite{Ellingsen2020}, and then some low differential uniformity functions were constructed. In this paper, we further study the constructions of perfect $c$-nonlinear (PcN) power functions. First, we give a necessary and sufficient condition for the Gold function to be PcN and a conjecture on all power functions to be PcN over $\gf(2^m)$. Second, several classes of PcN power functions are obtained over finite fields of odd characteristic for $c=-1$ and our theorems generalize some results in~\cite{Bartoli,Hasan,Zha2020}. Finally, the $c$-differential spectrum of a class of almost perfect $c$-nonlinear (APcN) power functions is determined.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
