In light of the exponential growth of digital technologies, ensuring information security has become increasingly critical. However, existing image encryption schemes often suffer from small key space, insufficient resistance to cryptanalysis, and low efficiency. To address these issues, this study proposes an innovative encryption approach based on a Six-Dimensional (6D) Hamiltonian hyperchaotic system. The system is constructed using Euler equations based on energy conservation analysis, with nonlinear transformations introduced to enhance complexity. Unlike traditional dissipative chaotic systems, Hamiltonian chaotic systems demonstrate enhanced phase-space coverage and higher resistance to reconstruction attacks due to energy conservation. The proposed system possesses at least two positive Lyapunov Exponents (LEs), ensuring greater chaotic complexity and randomness, thereby enhancing encryption security. Notably, this study is the first to identify the presence of multi-scroll orbit phenomenon in a 6D Hamiltonian hyperchaotic system. This phenomenon is confirmed via Poincaré section analysis, revealing the multi-folded and curled topological structures of chaotic trajectories in phase space. This discovery provides new dynamical insights for improving encryption algorithm security and expanding the key space (Formula: see text). For encryption design, a Gray-code-based bit-plane diffusion method, combined with a dual diffusion mechanism, is proposed to enhance pixel scrambling and diffusion. Security analyses and simulation findings confirm that the presented cryptographic method exhibits optimal performance across critical security indicators, including information entropy (Formula: see text bits), differential attack resistance (with average NPCR and UACI values of 99.611% and 33.478%, resp.), and robustness against noise and cropping attacks, demonstrating both strong security and practical applicability. It offers a promising solution for privacy protection in scenarios such as medical image transmission, social multimedia sharing, and IoT data security, highlighting its high security and practical value.
Liao et al. (Sat,) studied this question.