Design of a Four-Dimensional Discrete Chaotic Image Encryption Algorithm Based on Dynamic Adjacency Matrix

Chaotic systems, with their characteristics of high sensitivity to initial conditions, pseudo-randomness, and ergodicity, provide high-quality pseudo-random sequences. Graph theory, through mechanisms such as vertex mapping, path traversal, and graph partitioning, can enhance data confusion and diffusion capabilities. This research designs an image encryption method that combines graph theory and chaotic systems. Firstly, a four-dimensional discrete chaotic system is constructed based on the Hénon map, and its chaotic characteristics and high complexity over a wide range of parameters and initial values are verified using Lyapunov exponents and permutation entropy. Secondly, an encryption framework based on a dynamic adjacency matrix from graph theory is proposed: image pixels are mapped to a dynamic graph structure, and sparse adjacency matrices are generated using chaotic sequences to achieve pixel scrambling based on graph traversal; then, chaotic sequences are used for feedback diffusion with pixel values to enhance the confusion effect. Multiple sets of experiments verify its effectiveness and robustness in terms of key sensitivity, statistical analysis, resistance to differential attacks, and resistance to cropping attacks.