New Cost Function for S-boxes Generation by Simulated Annealing Algorithm

The simulated annealing algorithm relates to heuristic techniques for approximating optimization problems. It is well suited to finding a solution in a discrete state space. This algorithm simulates the physical processes that occur during metal annealing. While the temperature of the metal is high, the atoms of the substance can pass between the cells of the crystal lattice. As the substance cools, the probability of transitions decreases, and the process freezes. This is simulated in the computational algorithm for finding the global optimum. At each iteration, the simulated annealing algorithm forms several alternatives and chooses one of them. While the temperature is high, the adoption of worsening alternatives is allowed. As the temperature drops, the probability of worsening steps decreases. Cost functions are used to evaluate and compare possible alternatives. We are looking at the computational problem of generating S-boxes in the space of all 8-bit permutations. This is a difficult task, because the search space is very large – there are 256! permutations. We offer a new cost function that reduces the difficulty of finding S-boxes by an algorithm simulated annealing. Generated S-boxes can be used in cryptographic applications, such as symmetric key encryption algorithms and hash functions. Our experiments show that the new cost function allows you to quickly generate highly nonlinear S-boxes for cryptographic applications. For the simulated annealing algorithm, we obtained the best result, and this is the main contribution of this work.