Non-degenerate multi-stable discrete chaotic system for image encryption

The design of cryptographic algorithms using the chaos theory has become a hotspot in the field of information security. However, existing chaotic systems are prone to chaotic degradation, and generally do not exhibit multi-stability. In view of these issues, we first propose a non-degenerate multi-stable discrete chaotic system (NMDCS). After a rigorous theoretical analysis, it is proved that the NMDCS has an infinite number of unstable fixed points, and the number of positive Lyapunov exponents (LE) is equal to the system dimensions, indicating that the system has an infinite number of coexisting attractors and is not susceptible to chaotic degradation. In addition, Simulation experiments demonstrate that the NMDCS displays significant chaotic behavior and high efficiency. Finally, to satisfy the confidentiality protection demands for sensitive images, an efficient image encryption algorithm is designed by combining the NMDCS with an adaptive zigzag transformation method. Simulation experiments demonstrate that our image encryption algorithm has high efficiency in both encryption and decryption processes. Moreover, it demonstrates excellent security properties.