An image encryption scheme based on an improved Hilbert curve and a novel 4D hyper-chaotic system

• Designing a 4D hyperchaotic system exhibiting stronger chaos characteristics. • Building upon the Hilbert curve, we propose an improved version. • A new block diffusion method is developed using the proposed 4D hyperchaotic system. • Proposing a highly efficient and secure image privacy protection scheme. As one of the most information-rich forms of multimedia data, images are widely applied across numerous fields. However, during transmission, images are highly vulnerable to various attacks, making image encryption critically important. To address this challenge, this paper proposes a novel image encryption scheme based on a novel 4D hyperchaotic system and an improved Hilbert curve permutation strategy. First, a novel 4D hyperchaotic system with rich dynamical characteristics is introduced, whose complexity and pseudo-randomness are validated through Lyapunov exponent analysis and NIST randomness tests. Second, a novel space-filling curve is designed based on the Hilbert curve, which effectively enhances the confusion and randomness of the encrypted images. Finally, an intra-block diffusion algorithm driven by rotation and chaotic dynamics is employed to eliminate strong pixel correlations. Experimental analyses demonstrate that the Number of Pixels Change Rate (NPCR) and Unified Average Changing Intensity (UACI) reach approximately 99.6094% and 33.4645%, respectively, while the information entropy exceeds 7.990 and the key space is on the order of 2 443 . The experimental results indicate that the proposed scheme demonstrates measurable resistance against various attacks, showing competitive performance in terms of security and robustness.