Several classes of PcN power functions over finite fields.

Recently, a new concept called multiplicative differential cryptanalysis and the corresponding c -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 c -nonlinear (PcN) power functions. First, we give 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 Bartoli and Timpanella (2020), Hasan et al. (2021) and Zha and Hu (2021). Finally, the c -differential spectrum of a class of almost perfect c -nonlinear (APcN) power functions is determined. [ABSTRACT FROM AUTHOR]