A Novel Quaternionic Integer Reversible Dual-Hahn Transform and a New Hyperchaotic System for Medical Image Protection via Zero-Watermarking

Discrete orthogonal moments, such as the dual-Hahn moments, often exhibit limitations in accurately reconstructing signals, which reduces their effectiveness in applications that require precise recovery, particularly for 1D signals and color images. To address this limitation, this paper introduces a novel transform called the quaternionic integer reversible dual-Hahn transform (QIRDHT). This innovative approach enables simultaneous and lossless processing of 1D signals and color images, while being particularly well suited for resource-constrained environments. Furthermore, chaotic systems play a crucial role in cryptography, especially for secure key generation. However, the classical Hénon system has several drawbacks, including a restricted range of control parameters, limited sensitivity to initial conditions, and a tendency to generate periodic sequences. To overcome these limitations, we propose an enhanced hyperchaotic system that combines the dynamics of the Hénon system and logistic maps. This new hyperchaotic system exhibits richer dynamic behavior and a broader range of control parameters, significantly improving the security of encryption schemes. By integrating QIRDHT with this hyperchaotic map, we develop an efficient scheme for generating and extracting multiple zero-watermarks. The robustness of the proposed algorithm is evaluated against various geometric and common signal processing attacks using different medical images. Experimental results demonstrate that the proposed method outperforms existing approaches in terms of PSNR, BER, and NC, ensuring enhanced protection of medical images.