Construction of a New Discrete Chaotic Mapping Based on the Robust Chaos Theorem

Chaotic systems serve as fundamental pseudo-random sequence generators in encryption algorithms and play a vital role in communication security. However, most current research still focus on the classical Logistic chaotic map, making it vulnerable to targeted attacks. To address this issue, this paper proposes a general construction method for a class of cubic chaotic maps over the real number field and proves the existence of chaos based on the robust chaos criterion for S-unimodal maps. Furthermore, by integrating the proposed cubic chaotic map with the infinite folding map, a new one-dimensional discrete chaotic map is developed. Dynamical analysis demonstrates that, compared with the infinite folding map and the Logistic map, the newly constructed map exhibits stronger chaotic behavior and more stable complexity, showing superior potential for practical applications in secure communications.