Quad Key-Secured 3D Gauss Encryption Compression System with Lyapunov Exponent Validation for Digital Images

High-dimensional systems are more secure than their lower-order counterparts. However, high security with these complex sets of equations and parameters reduces the transmission system’s processing speed, necessitating the development of an algorithm that secures and makes the system lightweight, ensuring that the processing speed is not compromised. This study provides a digital image compression–encryption technique based on the idea of a novel quad key-secured 3D Gauss chaotic map with singular value decomposition (SVD) and hybrid chaos, which employs SVD to compress the digital image and a four-key-protected encryption via a novel 3D Gauss map, logistic map, Arnold map, or sine map. The algorithm has three benefits: First, the compression method enables the user to select the appropriate compression level based on the application using a unique number. Second, it features a confusion method in which the image’s pixel coordinates are jumbled using four chaotic maps. The pixel position is randomized, resulting in a communication-safe cipher text image. Third, the four keys are produced using a novel 3D Gauss map, logistic map, Arnold map, or sine map, which are nonlinear and chaotic and, hence, very secure with greater key spaces ($2^{498}$). Moreover, the novel 3D Gauss map satisfies the Lyapunov exponent distribution, which characterizes any chaotic system. As a result, the technique is extremely safe while simultaneously conserving storage space. The experimental findings demonstrate that the method provides reliable reconstruction with a good PSNR on various singular values. Moreover, the applied attacks demonstrated in the result section prove that the proposed method can firmly withstand the urge of attacks.