Generation of Nonlinear Substitutions by Simulated Annealing Algorithm

The problem of nonlinear substitution generation (S-boxes) is investigated in many related works symmetric key cryptography. In particular, the strength ciphers to linear cryptanalysis directly nonlinearity substitution. addition being highly nonlinear, S-boxes must be random, i.e., not contain hidden mathematical constructs that facilitate algebraic cryptanalysis. such substitutions a complex combinatorial optimization problem. Probabilistic algorithms are used solve it, for instance simulated annealing algorithm, which well-fitted discrete search space. We propose new cost function based on Walsh–Hadamard spectrum computation, and investigate efficiency using algorithm. For this purpose, we conduct numerous experiments with different input parameters: initial temperature, cooling coefficient, number internal external loops. As results research show, applying allows rapid substitutions. To find 8-bit bijective 104, need about 83,000 iterations. At same time, probability finding target result 100%.