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

Abstract

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