Several classes of PcN power functions over finite fields

04/27/2021

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by   Xiaoqiang Wang, et al.

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Recently, a new concept called multiplicative differential cryptanalysis and the corresponding c-differential uniformity were introduced by Ellingsen et al. <cit.>, 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 (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 <cit.>. Finally, the c-differential spectrum of a class of almost perfect c-nonlinear (APcN) power functions is determined.