Higher Order $c$-Differentials

TL;DR

This paper introduces higher order $c$-differentials, extending the concept of $c$-differentials in cryptanalysis, and analyzes their properties and impact on specific cryptographic functions.

Contribution

It proposes the notion of higher order $c$-derivatives and differentials, expanding the framework of differential cryptanalysis and analyzing their effects on key cryptographic functions.

Findings

Higher order $c$-differentials generalize existing differential concepts.

The paper analyzes the $c$-differential uniformity of inverse and Gold functions.

Results suggest new avenues for cryptanalysis using higher order differentials.

Abstract

EFRST20, the notion of $c$-differentials was introduced as a potential expansion of differential cryptanalysis against block ciphers utilizing substitution boxes. Drawing inspiration from the technique of higher order differential cryptanalysis, in this paper we propose the notion of higher order $c$-derivatives and differentials and investigate their properties. Additionally, we consider how several classes of functions, namely the multiplicative inverse function and the Gold function, perform under higher order $c$-differential uniformity.