Discrete Applied Mathematics ( IF 1.0 ) Pub Date : 2022-09-09 , DOI: 10.1016/j.dam.2022.08.022 Xiaoqiang Wang , Dabin Zheng , Lei Hu
Recently, a new concept called multiplicative differential cryptanalysis and the corresponding -differential uniformity were introduced by Ellingsen et al. (2020), and then some low differential uniformity functions were constructed. In this paper, we further study the constructions of perfect -nonlinear (PcN) power functions. First, we give a conjecture on all power functions to be PcN over . Second, several classes of PcN power functions are obtained over finite fields of odd characteristic for and our theorems generalize some results in Bartoli and Timpanella (2020), Hasan et al. (2021) and Zha and Hu (2021). Finally, the -differential spectrum of a class of almost perfect -nonlinear (APcN) power functions is determined.
中文翻译:
有限域上的几类 PcN 幂函数
最近,一个称为乘法差分密码分析的新概念和相应的-Ellingsen 等人介绍了差异均匀性。(2020),然后构造了一些低微分均匀性函数。在本文中,我们进一步研究了完美的构造-非线性(PcN)幂函数。首先,我们猜想所有的幂函数都是 PcN over. 其次,在奇特性的有限域上获得了几类 PcN 幂函数我们的定理概括了 Bartoli 和 Timpanella (2020)、Hasan 等人的一些结果。(2021 年)和查和胡(2021 年)。最后,-几乎完美的一类微分谱-确定非线性(APcN)幂函数。