Highly compressed image encryption algorithm via fractal and semi-tensor product compressed sensing

Storage space and security concerns on multimedia images have emerged as a global issue in recent years. Image encryption algorithm via compressed sensing (CS) is an effective method for data security and reducing storage space. However, the existing CS-based image encryption still faces problems, such as weak resistance to attacks and extensive data storage. We design a high-compression image encryption algorithm that combines fractal and semi-tensor product compressed sensing. First, a measurement matrix required for CS is generated using fractal blocks combined with the semi-tensor product method, which enhances security while reducing the size of the measurement matrix. Then, the measurements obtained from the sampling are used to define the product features of their mean and standard deviation. Exclusion criteria are set, and fractal codes are obtained through matched searching. Finally, the fractal code undergoes scrambling and diffusion, providing triple-layer protection and further improving the security of the secret image. In comparison to conventional methods, our proposed method has greatly improved the compression efficiency through compressed sampling and has the advantages of better concealment and enhanced robustness. Experiments show that we substantiate the effectiveness and superior performance of our method, all while upholding image quality and security.