Optimized simulated annealing for efficient generation of highly nonlinear S-boxes

S-boxes, the key nonlinear component in numerous cryptographic systems, play a crucial role in ensuring security. The quest for random highly nonlinear S-boxes, a desirable attribute for better diffusion and confusion properties, is, therefore, a critical endeavor in cryptographic research. However, generating such nonlinear S-boxes often involves significant computational effort, presenting a major challenge for researchers. This paper addresses this gap by proposing an optimized version of the Simulated Annealing (SA) algorithm specifically tailored for efficient generation of highly nonlinear S-boxes. Our work introduces a multithreaded implementation of the SA algorithm, a heuristic search method known for its proficiency in combinatorial optimization. The multithreading feature enhances computational efficiency, making our approach more suitable for large-scale cryptographic applications. We further optimize the algorithm by incorporating additional exit criteria for both internal and external loops, which significantly reduces the computational complexity associated with the nonlinear substitution generation process. Furthermore, we undertake comprehensive experiments to identify the optimal parameters of the SA algorithm, aiming to maximize the probability of generating target S-boxes while minimizing the number of iterations. This optimization step provides a clear pathway to improve the success rate of the generation process. The results of our study demonstrate a significant improvement over previous works, showing a 30–40% enhancement in the generation of nonlinear S-boxes.