Chaotic encryption algorithm with scrambling diffusion based on the Josephus cycle

Digital images are characterized by high redundancy and strong interpixel correlation. Breaking the correlation between data and improving sensitivity are crucial to protecting image information. To effectively achieve this goal, a chaotic encryption algorithm based on Josephus cycle scrambling diffusion is proposed in this paper. First, the adaptive key is generated by the Hash function to generate the initial value of the chaotic system, which is highly related to the plaintext image. The generation of the adaptive key can effectively resist plaintext attacks. Second, the pseudorandom sequence generated by the two-difference chaotic mapping is applied as the step sequence and direction sequence of Josephus traversal and optimizes Josephus traversal via variable steps and directions; the ranks of plain-text images are scrambled by the Josephus cycle to break the strong correlation between pixels. Finally, the initial cipher-text is divided into blocks to complete the Josephus cycle scrambling diffusion of image blocks, intrablock pixel bits and bit planes. The double permutations at the pixel level and bit level break the high correlation between pixels. Compared with the previous studies, our algorithm's average entropy of encrypted images is 7.9994, which has slightly improved. The correlation coefficient of the cryptographic image fluctuates up and down by approximately 0. In addition, the algorithm has the advantages of a large key space, high key sensitivity, anti-robust attack, and feasible encryption efficiency.