Fractal sorting matrix and its application on chaotic image encryption

Abstract

This article creatively proposes a class of sorting matrices with fractal characteristics, named the fractal sorting matrix (FSM), and introduces its iterative calculation method. The FSM is irregular, self-similar and infinitely iterative. Notably, scrambling images or information based on this new cluster of matrices can effectively improve encryption algorithm security. Then, the article presents a new method of global pixel diffusion with two chaotic sequences, which offers good security and high encryption efficiency. Based on the FSM and global chaotic pixel diffusion, this paper constructs a more efficient and secure chaotic image encryption algorithm than other approaches. According to experimental comparison, the proposed algorithm is faster and has a higher pass rate associated with the local Shannon entropy. The data in the antidifferential attack test are closer to the theoretical values and smaller in data fluctuation, and the images obtained from the cropping and noise attacks are clearer. Therefore, the proposed algorithm shows better security and resistance to various attacks.