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

TL;DR

This paper introduces new classes of non-monomial permutations over binary fields with low $c$-differential uniformity, advancing cryptographic functions resistant to differential attacks.

Contribution

It presents the first known non-monomial permutations with low $c$-differential uniformity over finite fields of even characteristic.

Findings

Proposed new classes of almost perfect $c$-nonlinear non-monomial permutations.

These permutations exhibit low $c$-differential uniformity.

Enhances cryptographic design by providing functions resistant to differential cryptanalysis.

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.