Design and implementation of dynamic s-boxes based on non-degenerate discrete chaotic systems

Abstract

Abstract In recent years, digital chaotic systems have received considerable attention in the field of secure communications. However, during the digitalization of the system, the original properties of the chaotic system may change, resulting in the degradation of the dynamics. To address this problem, this paper designs a novel simplicial non-degenerate discrete chaotic system based on the inverse hyperbolic tangent function, and selects a three-dimensional discrete system as the object of analysis. Through the research conducted, it is found that the chaotic system exhibits high Lyapunov exponents under certain conditions. Furthermore, the excellent randomness of the system has been further validated by NIST SP800-22 tests. At the same time, this paper also proposes a dynamic S-box construction method based on the chaotic sequence generated from the three-dimensional chaotic mapping. By performing a series of basic operations and permutation treatment, many dynamic S-boxes can be generated. This paper comprehensively analyses the performance of S-boxes from two perspectives: single S-boxes and multiple S-boxes. The analysis covers issues such as bijective property, nonlinearity, strict avalanche criterion, differential approximation probability and bit independence criteria. The results of the performance analysis show that the dynamically generated S-boxes have excellent cryptographic properties, making them suitable for the design and application of cryptographic algorithms.