Some classes of functions with low c-differential uniformity over finite fields.

Multiplicative differential (and the corresponding c-differential uniformity) was introduced by Ellingsen <italic>et al</italic>. in [C-differentials, multiplicative uniformity and (almost) perfect c-nonlinearity, <italic>IEEE Trans. Inf. Theory</italic> <bold>66</bold>(9) (2020) 5781–5789], which has attracted lots of attention. Functions with low c-differential uniformity over finite fields, especially the PcN and APcN functions, have been widely investigated due to their applications in cryptography. In this paper, we first compute the c-differential uniformity of two classes of permutation polynomials. For one of these, we explicitly determine the c-DDT entries. For the second type of function, we give bounds for its c-differential uniformity. Besides, several classes of PcN or APcN functions are presented by employing some known functions and the (generalized) AGW criterion. [ABSTRACT FROM AUTHOR]