Authors:
Pål Ellingsen
1
;
Constanza Riera
1
;
Pantelimon Stănică
2
and
Anton Tkachenko
1
Affiliations:
1
Department of Computer Science, Electrical Engineering and Mathematical Sciences, Western Norway University of Applied Sciences, 5020 Bergen, Norway
;
2
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943–5216, U.S.A.
Keyword(s):
Boolean, p-Ary Functions, c-Differentials, Walsh Transform, Differential Uniformity, Perfect and Almost Perfect c-Nonlinearity, Strict Avalanche Criterion.
Abstract:
The Strict Avalanche Criterion (SAC) is a property of vectorial Boolean functions that is used in the construction of strong S-boxes. We generalize in this paper the concept of SAC in the realm of finite fields, to address possible c-differential attacks. 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 find out, computationally, that the new definition is not equivalent to the existing concepts of c-bent1-ness (Stănică et al., 2020), nor (for n = m) PcN-ness (Ellingsen et al., 2020).