Design of highly nonlinear substitution boxes based on I-Ching operators

This paper is to design substitution boxes (S-Boxes) using innovative I-Ching operators (ICOs) that have evolved from ancient Chinese I-Ching philosophy. These three operators-intrication, turnover, and mutual-inherited from I-Ching are specifically designed to generate S-Boxes in cryptography. In order to analyze these three operators, identity, compositionality, and periodicity measures are developed. All three operators are only applied to change the output positions of Boolean functions. Therefore, the bijection property of S-Box is satisfied automatically. It means that our approach can avoid singular values, which is very important to generate S-Boxes. Based on the periodicity property of the ICOs, a new network is constructed, thus to be applied in the algorithm for designing S-Boxes. To examine the efficiency of our proposed approach, some commonly used criteria are adopted, such as nonlinearity, strict avalanche criterion, differential approximation probability, and linear approximation probability. The comparison results show that S-Boxes designed by applying ICOs have a higher security and better performance compared with other schemes. Furthermore, the proposed approach can also be used to other practice problems in a similar way.