Dynamical analysis of a novel chaotic system and its application to image encryption

Abstract

This study presents a novel four-dimensional chaotic system derived from the Lorenz-Haken equation. The paper investigates the system’s dissipative properties, equilibrium point, Poincaré map, 0–1 test, Lyapunov exponent, complexity, and bifurcation diagram to introduce the system’s dynamics. The research also examines the chaotic behavior of the system under various parameters, demonstrating the existence of symmetric attractors and offset boosting. To demonstrate the system’s feasibility, circuit simulation is performed using Multisim software, and the hardware implementation is carried out using a Field Programmable Gate Array (FPGA). An image encryption algorithm is designed by integrating matrix dislocation, backward diffusion, and deoxyribonucleic acid (DNA) encryption with the discretized chaotic system. The simulation results show that the algorithm has a good encryption effect. NIST tests show that the sequence has good randomness, correlation coefficient, and information entropy tests show that the encrypted image has strong randomness, and key space and key sensitivity prove that the system has a good ability to resist exhaustive attacks. The use of simulated differential attacks, cropping attacks, and noise attacks has demonstrated the high robustness of the system. The use of peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index proves that the encryption algorithm does not affect image quality. Further proving the excellent performance of the proposed encryption algorithm.