Functions with low c-differential uniformity have optimal resistance to some types of differential cryptanalysis. In this paper, we investigate the c-differential uniformity of power functions over finite fields of odd characteristic. Based on some known almost perfect nonlinear functions, we present several classes of power functions \(f(x)=x^d\) with \(_{c}\varDelta _f\le 3\). Especially, two new classes of perfect c-nonlinear power functions are proposed.

中文翻译：

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在有限域上具有低c微分均匀性的几类幂函数

具有低c差分均匀性的函数对某些类型的差分密码分析具有最佳的抵抗力。在本文中，我们研究了奇特性有限域上幂函数的c微分均匀性。基于一些已知的几乎完美的非线性函数，我们提出了几类具有\（_ {c} \ varDelta _f \ le 3 \）的幂函数\（f（x）= x ^ d \）。特别是，提出了两类新的理想的c非线性幂函数。