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), then some low functions constructed. In this paper, we further study constructions of perfect c-nonlinear (PcN) power functions. First, give conjecture on all to be PcN over GF(2m). Second, several classes are obtained finite fields odd characteristic for c=−1 our theorems generalize results in Bartoli Timpanella Hasan (2021) Zha Hu (2021). Finally, spectrum class almost (APcN) is determined.