Color image encryption algorithm based on ∞-shaped transformation and closed-loop control model

As color images have become a cornerstone of information exchange in the digital age, ensuring their security is of paramount importance. With the traditional scrambling-diffusion structure, this paper proposes a novel color image encryption algorithm by integrating of an ∞ -shaped transformation with a closed-loop control mechanism. First, the three channel matrices are merged, and the elements in each row are linked into a closed loop for initial diffusion. Secend, the diffused image is subsequently restructured into a three-row matrix and scrambled using a unique ∞ -shaped transformation. Finally, column-wise closed-loop diffusion is applied to generate the cipher image. This algorithm not only achieves effective inter-channel pixel confusion through the ∞ -shaped transformation, but also performs additional diffusion and confusion under the closed-loop control model. Experimental results demonstrate the algorithm's excellent overall performance: the key space is as large as 2413, information entropy approaches the ideal value of 8 with increasing image size, and the algorithm exhibits high sensitivity, with NPCR and UACI exceeding 99.6% and 33.4%, respectively. Quantitative evaluation confirms that the proposed algorithm offers strong robustness against differential, statistical, and brute-force attacks.