Integer reversible Racah transform and enhanced chaotic maps for 1D/2D signal reconstruction and secure image encryption

Traditional discrete orthogonal transforms, such as the Racah transform, often lead to reconstruction errors, limiting their application in digital signal processing tasks that require exact signal recovery. To overcome this limitation, this article introduces the Integer Reversible Racah Transform (IRT), a novel integer-based discrete transform specifically designed for lossless signal processing on resource-constrained platforms. Additionally, considering the significant role of chaotic systems in encryption, we propose an enhanced chaotic scheme that improves upon the logistic map-based chaotic model. The classical logistic map has cryptographic limitations due to its single control parameter, narrow sensitivity range to initial conditions, and the potential periodicity of generated sequences. To address these issues, the proposed chaotic map in this study offers a broader chaotic interval and an expanded control parameter space, ensuring more secure key generation for encryption systems. By combining the IRT with our proposed chaotic system, we develop an efficient encryption and decryption scheme. Experimental results demonstrate that this scheme provides substantial resistance against various attacks while maintaining nearly intact quality in decrypted images. This highlights not only the effectiveness of the encryption scheme but also its enhanced security and robustness. Compared to existing methods, our scheme stands out for its exceptional reliability and robustness, significantly contributing to the secure protection of images.