Optimizing the Local Search Algorithm for Generating S-Boxes

Nonlinear substitutions (S-boxes) are an important component of modern symmetric cryptography algorithms. They complicate symmetric transformations and introduce nonlinearity in the input-output relationship, which provides resistance to some cryptanalysis techniques. S-boxes generation can be done in a number of ways. However, the most promising are heuristic techniques. On the one hand, the generated S-boxes look like random settings, which complicates algebraic cryptanalysis. On the other hand, heuristic search makes it possible to achieve high nonlinearity and δ-uniformity, which complicates linear and differential cryptanalysis. In this article, we will explore the simplest local search algorithm for generating S-boxes. To assess the efficiency of the algorithm, the concept of a track of a cost function is introduced in the article. We optimize the algorithm parameters and show that with the chosen parameters it is possible to reliably form S-boxes with nonlinearity 104.