Investigations on $c$-(almost) perfect nonlinear functions

TL;DR

This paper explores the properties of $c$-almost perfect nonlinear functions, extending differential cryptanalysis by analyzing their $c$-differential uniformity, especially in APN functions, revealing significant increases in some cases.

Contribution

It introduces and investigates the $c$-differential uniformity of APN functions, expanding understanding of their cryptanalytic properties.

Findings

$c$-differential uniformity can increase significantly for some APN functions

The concept extends traditional differential cryptanalysis methods

Provides new insights into the security of cryptographic functions

Abstract

In a prior paper \cite{EFRST20}, two of us, along with P. Ellingsen, P. Felke and A. Tkachenko, 1defined a new (output) multiplicative differential, and the corresponding $c$-differential uniformity, which has the potential of extending differential cryptanalysis. Here, we continue the work, by looking at some APN functions through the mentioned concept and showing that their $c$-differential uniformity increases significantly, in some cases.