Image compression and encryption algorithm based on uniform non-degeneracy chaotic system and fractal coding

This paper focuses on the design of chaotic image compression encryption algorithms. Firstly, we design a uniform non-degenerate chaotic system based on nonlinear filters and the feed-forward and feed-back structure. Theoretical and experimental analyses indicate that the system can avoid the drawbacks of the existing chaotic systems, such as chaos degradation, uneven trajectory distribution, and weak chaotic behavior. In addition, our chaotic system can produce chaotic sequences with good pseudo-random characteristics. Then, we propose a fractal image compression algorithm based on adaptive horizontal or vertical (HV) partition by improving the baseline HV partition and the time-consuming global matching algorithm. The algorithm does not need to implement time-consuming global matching operations. In addition, analysis results demonstrate that our fractal image compression algorithm can reconstruct the original image with high quality under ultra-high compression ratios. Finally, to protect the confidentiality of images, we propose a chaotic fractal image compression and encryption algorithm by using our chaotic system and fractal image compression algorithm. The algorithm achieves excellent diffusion and confusion abilities without using the hash value of plain images. Therefore, it avoids the failure of decryption caused by the tampering of hash value during the transmission process, and can well resist differential attacks and chosen-ciphertext attacks. In addition, simulation results show the algorithm is efficient and robust.