Non-Boolean almost perfect nonlinear functions on non-Abelian groups

TL;DR

This paper extends the concepts of APN and maximum nonlinear Boolean functions to mappings between non-Abelian groups, broadening the theoretical framework for cryptographic functions beyond Abelian groups.

Contribution

It introduces extended definitions and characterizations of APN and maximum nonlinear functions for non-Abelian group mappings, a novel generalization in cryptography.

Findings

Extended definitions of APN for non-Abelian groups

Characterizations of maximum nonlinear functions in non-Abelian context

Framework for analyzing cryptographic functions on non-Abelian groups

Abstract

The purpose of this paper is to present the extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions to deal with the case of mappings from a finite group K to another one N with the possibility that one or both groups are non-Abelian.