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 generalizes the notion of differential uniformity measuring the resistance against 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 present new classes of (almost) perfect c-nonlinear non-monomial permutations over a binary field.