Robust Image Encryption Exploiting 2D Hyper-Chaos, Fractal Sierpiński Carpet Confusion, and Cascaded Diffusion

With the rapid growth of digital image transmission, ensuring data security has become increasingly important. However, existing chaos-based image encryption algorithms often suffer from insufficient chaotic randomness and weak integration between chaotic dynamics and encryption mechanisms. To address these issues, a novel image encryption scheme based on a two-dimensional hyperbolic–exponential Sine–Logistic map (2D-HESLM) is proposed. A Sierpiński carpet-inspired scrambling strategy and a cascaded diffusion mechanism are designed to enhance permutation and diffusion performance based on the 2D-HESLM. The experimental results show that the information entropy value is 7.9980, while NPCR and UACI are approximately averaged 99.6147% and 33.4672%, respectively, with correlation coefficients close to zero. These results demonstrate the effectiveness and security of the proposed scheme.