WHS Cost Function for Generating S-boxes

Nonlinear substitution boxes (S-boxes) use in most modern symmetric cryptoalgorithms. They are designed to mix input data and take the essential part in ensuring resistance against known cryptoanalytic attacks (differential, linear, algebraic and other methods of cryptoanalysis). However, the random formation of nonlinear substitutions with the required rates is an extremely complex mathematical problem. We observe the heuristic techniques of S-boxes informed search, in particular, we consider the cost function used in most known algorithms (eg, local search, gradient lift, annealing simulation, genetic search, etc.). The purpose of our research is to determine the specific parameters of the heuristic function, which on the one hand do not reduce the degree of awareness of search nodes, and on the other hand do not require significant computational costs. We investigate the influence of individual parameters on the value of the cost function and on the complexity of its calculation. We also provide specific recommendations for the formation of parameters for the heuristic search of S-boxes.