Affiliation:
1. School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P. R. China
2. Key Laboratory of Mathematical Modelling and High Performance, Computing of Air Vehicles (NUAA), MIIT, Nanjing 211106, P. R. China
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.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jiangsu Province
Outstanding Doctoral Dissertation in NUAA
Publisher
World Scientific Pub Co Pte Ltd