A chaotic image encryption algorithm based on a counting system and the semi-tensor product

Abstract

Based on the n-ary counting system, combined with the matrix semi-tensor product theory and Hilbert curve, a chaotic image encryption algorithm is designed. Different from the traditional encryption method, the algorithm proposed in this paper is an encryption algorithm with scrambling and diffusion at the same time. First, the pixel value is converted from decimal to n-ary. In the n-ary counting system, the plaintext image is randomly divided into some groups, and the Hilbert curve is used for scrambling to each group. The blocks are converted into scrambled images, so that the scrambling and diffusion can be carried out at the same time. Then, in order to improve the security of the algorithm, another round of diffusion is carried out based on matrix semi-tensor product mechanism. Chaotic sequence is generated by Chen system. This chaotic sequence performs matrix semi-tensor product operation with the first round of encrypted image, and generate second encrypted images. Finally, this encryption method is applied to color image encryption. Compared with some representative algorithms, the experimental results show that the algorithm proposed in this paper is secure and it can resist common attacks.