On non-monomial APcN permutations over finite fields of even characteristic

Abstract

Recently, a new concept called the $c$-differential uniformity was proposed by Ellingsen et al. (2020), which allows to simplify some types of differential cryptanalysis. Since then, finding functions having low $c$-differential uniformity has attracted the attention of many researchers. However it seems that, at this moment, there are not many non-monomial permutations having low $c$-differential uniformity. In this paper, we propose new classes of almost perfect $c$-nonlinear non-monomial permutations over a binary field.

We made a revised version, where Sec 4 was revised as follows: G_alp(x) is newly introduced and Theorem 4.12 is added