A Secure Medical Image Encryption Scheme Based on Cross-Ring Josephus Scrambling and Two-Dimensional Cellular Automata

With the rise of telemedicine and intelligent diagnostics, the efficiency and accuracy of healthcare services have been significantly enhanced. However, the highly sensitive nature of medical images makes protecting patient privacy during transmission and storage a critical challenge. In this paper, we propose a secure medical image encryption scheme based on cross-ring Josephus scrambling and two-dimensional cellular automata, designed to safeguard medical images. First, we introduce a novel two-dimensional chaotic map (2D-CICM) with an expanded parameter range to generate high-quality key sequences for encryption. Next, we design a cross-ring Josephus scrambling algorithm for pixel permutation, where the eliminated pixel is determined by both inter-ring and intra-ring step sizes. Following this, we develop a diffusion mechanism based on interaction rules defined by six types of two-neighbor structures within a cellular automaton framework. To enhance key sensitivity and image-specific security, we also incorporate the 512-bit hash value of the plaintext image to dynamically update the initial keys, ensuring that the encryption key sequences are unique for each image. Comprehensive security analyses and performance evaluations confirm that the proposed scheme provides strong encryption performance and effectively resists common attacks, while maintaining computational efficiency suitable for medical applications.