A Low-Complexity 4D Discrete Chaotic System for Secure Image Encryption Based on Reversible Neural Network
Han Chen, Qingye Huang, Yingjie Su, Lezhu Chen, Baoyi Liao, Linqing Huang, Changwen Chen · Entropy · 2026
To address the limitations of existing chaotic systems such as complex structure and potential chaotic degradation, this paper proposes a novel four-dimensional discrete chaotic system (4D-DCS) and an image encryption algorithm based on it. The 4D-DCS is constructed by integrating a feedback controller and modulo operation into a linear discrete-time system, featuring a simple structure without the need for intricate matrix reconstruction or memristor circuits. Mathematical analysis confirms its chaos in the sense of Li-Yorke and numerical simulations including Lyapunov exponent (LE) analysis, 0-1 test, and NIST SP 800-22 test demonstrate its hyperchaotic characteristics and excellent pseudorandomness. Based on the 4D-DCS, the proposed encryption algorithm employs SHA-256 to generate initial states for key uniqueness, combines row-column permutation to disrupt pixel correlation, and adopts a reversible neural network for diffusion to enhance confusion capability. Comprehensive security analysis shows that the algorithm achieves an NPCR of ∼99.61% and a UACI of ∼33.46%, a key space of 2216, information entropy close to 8, and correlation coefficients of encrypted images near 0. It also exhibits strong robustness against differential, cropping, noise, and chosen-plaintext attacks. Comparative analysis with state-of-the-art algorithms validates the 4D-DCS's advantages in structural simplicity and stability, and the encryption algorithm's superiority in security and practicality, making it suitable for security-critical applications such as image encryption.