A Novel Image Shift Encryption Algorithm Based on the Dynamic Joseph Ring Problem

Image encryption can effectively prevent unauthorized users from stealing personal information. Attackers usually analyze the information of the encrypted image according to the strong correlation between image pixels and use it as the breakthrough point of the image encryption algorithm. How to destroy the strong correlation of pixels is a hot topic of current research. In this paper, we propose a novel and simple encryption scheme that is no less effective than other algorithms, called Joseph shift encryption (JSE). To enhance the effectiveness of image encryption, we propose the static Joseph shift encryption (S-JSE) and the dynamic Joseph shift encryption (D-JSE) algorithms. S-JSE can decrease the dimension of the image and shift with the generated Joseph sequence group, then the encrypted image can be generated. D-JSE can increase the number of iterations on the basis of S-JSE, and the Joseph sequence of each iteration is different. Furthermore, the encrypted sequence is scrambled according to the Joseph mapping table and upgraded the dimension to complete the encryption. We analyze the effectiveness of the proposed S-JSE including the impact of the key selection on the effect of image encryption, and the encryption security. Thereafter, we utilize the proposed D-JSE to improve the security of grayscale and color image and verify the effectiveness of the proposed algorithm by extensive and comprehensive experiments in terms of correctness verification, histogram equalization and information entropy, adjacent pixel correlation, plaintext sensitivity, key sensitivity, encrypted image anti-interference, key space, encryption time and defense against special image attacks .