A Robust Memristor-Enhanced Polynomial Hyper-Chaotic Map and Its Multi-Channel Image Encryption Application

Nowadays, the utilization of memristors to enhance the dynamical properties of chaotic systems has become a popular research topic. In this paper, we present the design of a novel 2D memristor-enhanced polynomial hyper-chaotic map (2D-MPHM) by utilizing the cross-coupling of two TiO2 memristors. The dynamical properties of the 2D-MPHM were investigated using Lyapunov exponents, bifurcation diagrams, and trajectory diagrams. Additionally, Kolmogorov entropy and sample entropy were also employed to evaluate the complexity of the 2D-MPHM. Numerical analysis has demonstrated the superiority of the 2D-MPHM. Subsequently, the proposed 2D-MPHM was applied to a multi-channel image encryption algorithm (MIEA-MPHM) whose excellent security was demonstrated by key space, key sensitivity, plaintext sensitivity, information entropy, pixel distribution, correlation analysis, and robustness analysis. Finally, the encryption efficiency of the MIEA-MPHM was evaluated via numerous encryption efficiency tests. These tests demonstrate that the MIEA-MPHM not only possesses excellent security but also offers significant efficiency advantages, boasting an average encryption rate of up to 87.2798 Mbps.