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arXiv · 2104.12942

Several classes of PcN power functions over finite fields

Xiaoqiang Wang·Dabin Zheng
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Abstract

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.

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Xiaoqiang Wang, Dabin Zheng. 2021-04-27. Several classes of PcN power functions over finite fields. https://arxiv.org/abs/2104.12942

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