An effective method to improve nonlinearity value of substitution boxes based on random selection

Abstract

In today's digital society, new design alternatives are needed for substitution box structures, which has critical importance in developing secure information systems that are resistant to algebraic and application attacks, as new attacks negatively affect designs based on mathematical transformations. Although random selection-based substitution box structures are a good alternative against algebraic and application attacks, the low value of nonlinearity criterion is an important problem. Solution suggestions using optimization algorithms have been proposed to address this problem. “Information Sciences 523 (2020) 152–166” is the study that reached the highest nonlinearity value based on optimization algorithms to date. However, the high computational costs of optimization algorithms are another challenge that must be overcome. In this study, it has been shown that the nonlinearity values ​​of random (chaotic) selection substitution box structures can be improved as much as mathematically based designs by using a method that is too simple to compare with optimization algorithms. It has been shown that the nonlinearity value can be improved up to 110 for random selection-based substitution box designs. Although this nonlinearity value is the highest achievable value in the literature based on the random selection principle, the fact that it requires only 2×255×255 processes in the worst case has been evaluated as an important success of the proposed method compared to other design approaches. Other advantages of the proposed method are that the improved substitution box structures are resistant to side-channel attacks, simple structure, easy hardware implementation, and successful results in practical applications such as image encryption. It is believed that all these results will be a motivation for new post-processing techniques to be designed in the future for random selection-based substitution box designs.