Substantiation of the parameters of the annealing simulation algorithm for searching non-linear substitutions of symmetric ciphers

Cryptographic protection in information and information and communication systems is an important component of cybersecurity. Therefore, the development, research and improvement of means of cryptographic information protection is an urgent and important task. In this paper, we study evolutionary methods for generating non-linear substitutions (S-boxes). These are cryptographic primitives that are an important component of many modern block and stream ciphers with a secret key. However, the problem of generating random highly non-linear substitutions is extremely difficult. In this paper, we study the annealing simulation method. This is an iterative algorithm, the essence of which is the gradual improvement of the current solution (substitution). Special cost functions are used as an improvement criterion. The initial state is formed randomly, and then, at each iteration the current solution is gradually changed. Approaching the target solution means minimizing the cost function. The paper investigates a simple and computationally efficient cost function based on the Walsh-Hadamard transform. Through exploratory research and numerous tests, it was possible to optimize the operation of the annealing simulation algorithm. Optimized algorithm for several parameters (initial temperature, "cooling factor", cost function) allows you to quickly generate highly non-linear bijective substitutions for cryptographic applications. Compared to other well-known implementations of the annealing simulation algorithm, the use of the recommended parameters can significantly reduce the generation time of nonlinear substitutions.