Exploiting Four-Dimensional Chaotic Systems with Dissipation and Optimized Logical Operations for Secure Image Compression and Encryption

In this paper, a new four-dimensional chaotic system derived from the continuous Hopfield neural network (CHNN) model is designed, and the weight parameters are optimized to achieve superior dynamics. Furthermore, we verify the superior performance of the system through an analysis of its dissipation and other aspects. Meanwhile, to address the issues of low reconstruction quality and unsatisfactory security performance of the current compressed sensing (CS)-based image encryption algorithm, this paper introduces a compression encryption algorithm based on the chaotic system. Specifically, this algorithm designs a new fractal curve based on the Hilbert curve by incorporating a unique rotation and connection in the iterative process, which allows for effective displacement of the image. Additionally, a new measurement matrix with low spectral norm is constructed utilizing the QR decomposition based on the Householder transform to improve the compression performance. Finally, this paper introduces a bidirectional Z-shaped diffusion method based on chaotic sequences and optimized multiple logical operations (BZCM). By leveraging the optimized logic operation rules and logic key matrix proposed in this paper, this method enhances the diffusion effect. Experimental analyses demonstrate that the proposed algorithm achieves high security and reconstruction performance.