Abstract As a critical component in cryptographic algorithms, the S-box plays a crucial role in modern cryptography. In this paper, we first study the properties of traditional chaotic systems, design a one-dimensional chaotic system with an extensive parameter range and excellent chaotic properties, and design an initial chaotic S-box based on the system. Secondly, we create a Boolean function nonlinearity boosting algorithm based on the proposed Boolean function nonlinearity boosting theorem and a rolling Boolean S-box nonlinearity boosting theorem based on the proposed S-box nonlinearity boosting theorem. S-box nonlinearity boosting algorithm. In addition, for the constructed high nonlinear S-box, the other performances of the S-box are further optimized by a multi-objective optimization annealing algorithm. The best S-box obtained is analyzed for the performance of nonlinearity, strict avalanche, linear approximation probability, differential uniformity, and bit-independence criterion. We receive a high-performance S-box with a nonlinearity of 114.75. Finally, a high-performance S-box with a nonlinearity of 114.75 is designed. Image encryption that only relies on the S-box, and through the tests of the histogram, adjacent-pixels correlation, and information entropy, the results show that the generated high-performance S-box has a complex substitution effect, which is sufficient to meet the nonlinear design requirements of the packet encryption algorithm.
Cheng et al. (Mon,) studied this question.