SBOX-CGA: substitution box generator based on chaos and genetic algorithm

What makes artificial intelligence techniques so remarkable in the field of computer science is undoubtedly their success in producing effective solutions to difficult computational problems. In particular, metaheuristic optimization algorithms are a unique example of using artificial intelligence techniques to generate approximate solutions to problems that cannot be solved in polynomial time, called NP. Obtaining a substitution box (s-box) structure that will satisfy the desired requirements in cryptography is an example of these NP problems. In the literature, it is a hot topic to optimize the s-box structures obtained from chaotic entropy sources with heuristic algorithms to improve their cryptographic properties. The study with the highest nonlinearity value (110.25) based on optimization algorithms to date has been published in 2020. In this study, a method with a higher nonlinearity value than the algorithms previously proposed in the literature is developed. It has been shown that the nonlinearity value can be increased to 111.75. These results will be a basis for new research on the chaos-based s-box literature and will motivate new studies to develop alternative optimization algorithms in the future to obtain s-box structures based on the random selection equivalent to the AES s-box.