Optimization of local search algorithm parameters for generating nonlinear substitutions

Nonlinear substitutions (S-boxes) are an important component of modern symmetric cryptography algorithms. They complicate symmetric transformations and introduce nonlinearity into the input-output relationship, which ensures the stability of the algorithms against some cryptanalysis methods. Generation of S-boxes can be done in different ways. However, heuristic techniques are the most promising ones. On the one hand, the generated S-boxes are in the form of random substitutions, which complicates algebraic cryptanalysis. On the other hand, heuristic search allows one to achieve high rates of nonlinearity and δ-uniformity, which complicates linear and differential cryptanalysis. This article studies 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. Numerous experiments are carried out, in particular, the influence of the number of internal and external loops of local search on the complexity of generating the target S-box is investigated. The optimal (from the point of view of minimum time consumption) parameters of the local search algorithm for generating S-blocks with a target nonlinearity of 104 and the number of parallel computing threads 30 are substantiated. It is shown that with the selected (optimal) parameters it is possible to reliably form S-blocks with a nonlinearity of 104.