A new high-dimensional digital chaotic system and its S-box application

This paper is mainly devoted to developing a general framework for scalable high-dimensional digital chaotic systems to address the fundamental limitation of the dimensionality fixation of traditional chaotic systems. Our core research goal is to promote the theoretical and practical development of digital chaotic systems through state space topological reorganization, realize the free dimensionality extension of chaotic mapping, and strictly prove that it complies with the Devaney chaos criterion. We then selected one of the two-dimensional digital chaotic systems and verified its excellent randomness through comprehensive random statistical properties. In order to prove the feasibility of our digital chaotic system in practical applications, we further developed the S-box design method, achieved high-performance hardware acceleration on the ZYNQ platform, and achieved efficient transmission of calculation results through the AXI_Lite protocol. Experimental results show that our S-box design based on chaotic systems outperforms existing schemes in key indicators such as nonlinearity and differential uniformity, and significantly enhances the security and anti-attack capabilities of cryptographic components. This study solves the problem of dynamical degradation existing in traditional chaotic systems, contributes to the subsequent research of chaotic systems, and verifies its chaos and practical feasibility.