High-Speed Image Compression–Encryption Scheme Based on a New Chaotic Map and Improved Lifting Wavelet Transform

In resource-constrained communication environments, important image data needs to be compressed before encrypted transmission. This paper proposes effective solutions to this issue. Firstly, a new one-dimensional discrete chaotic system model was constructed based on the logistic system and fractional structure. Through theoretical analysis combined with numerical simulation experiments, it has been proven that the proposed new system has excellent chaotic characteristics. Compared with some traditional one-dimensional chaotic systems, the new system has a wider range of chaotic parameters and stronger complexity, making it more suitable for image data encryption. Secondly, a high-compression-ratio image compression method based on improved lifting wavelet transform and a fast image encryption algorithm based on the new chaotic map are proposed. Simulation experiments and security analysis results show that the proposed image compression–encryption scheme has excellent performance and less time overhead. It has good resistance to various cryptanalysis attacks and strong robustness to noise and data loss attacks, which indicates that the proposed image compression–encryption scheme has good application potential in resource-constrained communication environments. The main contribution of this article is the design of a new chaotic system model with practical performance and the development of a new application case. The main novelty of this paper is the proposal of a fast algorithm for high compression ratio and encryption of images.