Parallel Steepest Ascent Hill-Climbing for High Nonlinear Boolean and Vectorial Boolean Functions (S-Boxes)

Abstract

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 \(n \times m\) 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.