An extension of the avalanche criterion in the context of c-differentials
This work is incremental, extending cryptographic criteria for S-box construction to enhance security against specific differential attacks in finite fields.
The paper tackles the problem of generalizing the Strict Avalanche Criterion (SAC) to address c-differential attacks in finite fields, defining new concepts like c-SAC and c-SAC(m) and showing computationally that these are not equivalent to existing properties such as c-bent1-ness and PcN-ness.
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)