Boolean functions and their generalization Vectorial Boolean functions or Substitution Boxes (S-Boxes) have attracted much attention in the domain of modern block ciphers that use only these elements to provide the necessary confusion against the cryptanalysis attacks. Thus, a significant number of research has been done to construct cryptographically strong Boolean functions and S-Boxes. Among these researches, several heuristics were applied and therefore the hill climbing heuristic was largely investigated. In this paper, we propose a new variant of Hill Climbing heuristic called Parallel Steepest Ascent Hill Climbing to construct Boolean functions and (formula presented) S-Boxes through the progressive construction and incorporation of their m coordinate Boolean functions. The obtained results demonstrate that this new variant provides solutions with high cryptographic properties.
CITATION STYLE
Seghier, A., & Li, J. (2020). Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11999 LNCS, pp. 413–429). Springer. https://doi.org/10.1007/978-3-030-41579-2_24
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