A New Image Encryption Algorithm Based on Cantor Diagonal Matrix and Chaotic Fractal Matrix

Driven by advancements in mobile internet technology, images have become a crucial data medium. Ensuring the security of image information during transmission has thus emerged as an urgent challenge. This study proposes a novel image encryption algorithm specifically designed for grayscale image security. This research introduces a new Cantor diagonal matrix permutation method. The proposed permutation method uses row and column index sequences to control the Cantor diagonal matrix, where the row and column index sequences are generated by a spatiotemporal chaotic system named coupled map lattice (CML). The high initial value sensitivity of the CML system makes the permutation method highly sensitive and secure. Additionally, leveraging fractal theory, this study introduces a chaotic fractal matrix and applies this matrix in the diffusion process. This chaotic fractal matrix exhibits self-similarity and irregularity. Using the Cantor diagonal matrix and chaotic fractal matrix, this paper introduces a fast image encryption algorithm involving two diffusion steps and one permutation step. Moreover, the algorithm achieves robust security with only a single encryption round, ensuring high operational efficiency. Experimental results show that the proposed algorithm features an expansive key space, robust security, high sensitivity, high efficiency, and superior statistical properties for the ciphered images. Thus, the proposed algorithm not only provides a practical solution for secure image transmission but also bridges fractal theory with image encryption techniques, thereby opening new research avenues in chaotic cryptography and advancing the development of information security technology.