An extension of the avalanche criterion in the context of c-differentials

TL;DR

This paper extends the Strict Avalanche Criterion to c-differentials in finite fields, providing new definitions and computational insights relevant for cryptographic resistance against c-differential attacks.

Contribution

It introduces the c-Strict Avalanche Criterion and c-SAC(m), generalizing previous SAC concepts to address c-differential cryptanalysis.

Findings

c-SAC is not equivalent to c-bent1-ness

c-SAC differs from PcN-ness for n=m

New definitions enhance understanding of cryptographic properties

Abstract

The Strict Avalanche Criterion (SAC) is a property of vectorial Boolean functions that is used in the construction of strong S-boxes. We show in this paper how to generalize the concept of SAC to address possible c-differential attacks, in the realm of finite fields. We define the concepts of c-Strict Avalanche Criterion (c-SAC) and c-Strict Avalanche Criterion of order m (c-SAC(m)), and generalize results of (Li and Cusick, 2005). We also show computationally how the new definition is not equivalent to the existing concepts of c-bent1-ness (Stanica et al., 2020), nor (for n = m) PcN-ness (Ellingsen et al., 2020)