A Novel Multi-Image Encryption Scheme Using Generalized Rectangular Transform and Advanced 5-D Hyperchaotic Map

This paper presents GRTPHM (Generalized Rectangular Transform and Penta-Hyperchaotic Map), a novel multi-image encryption scheme that enhances security, efficiency, and versatility. The encryption process consists of two key phases: pixel permutation and pixel diffusion. The pixel permutation phase leverages the Generalized Rectangular Transform (GRT) to rearrange pixel positions using a flexible transformation matrix, effectively disrupting strong correlations between neighboring pixels and improving resistance to statistical analysis. In the pixel diffusion phase, a bit-level random permutation (BLRP) technique is employed alongside a Penta-Hyperchaotic Map (PHM), an advanced 5-D discrete memristor and meminductor-based hyperchaotic map, integrated with the SHA-512 hashing function. Unlike traditional pixel-based diffusion methods, BLRP shuffles bits, achieving finer confusion and making structural inference significantly more difficult for attackers. The PHM generates a highly unpredictable chaotic sequence, ensuring substantial changes in ciphertext even for minor modifications in plaintext or encryption parameters. This enhances the avalanche effect, strengthening resistance to differential and statistical attacks. GRTPHM introduces a novel reverse rectangular transform (IGRT) that overcomes the limitations of existing approaches, enabling efficient and accurate image reconstruction. Notably, decryption does not require prior knowledge of the transformation matrix’s periodicity and achieves a speedup of up to 299 times compared to state-of-the-art methods. Extensive robustness testing against cropping, salt & pepper noise, and hybrid attacks confirms that GRTPHM can maintain satisfactory decryption accuracy and visual quality, even under severe image distortions. The results indicate that cropping attacks cause greater degradation than noise-based attacks due to the irreversible loss of contiguous pixel regions. The scheme supports a wide range of image sizes and formats, including rectangular and equilateral images, as well as single and multi-image encryption scenarios. Performance evaluations demonstrate that GRTPHM outperforms existing encryption techniques in terms of accuracy, computational efficiency, security, and adaptability. Comparative analyses confirm its robust encryption and decryption capabilities, effectively protecting against chosen-plaintext and differential attacks. These results establish GRTPHM as a comprehensive and reliable solution for modern image encryption applications.