Enhanced Batch Medical Image Encryption Using an Improved Lorenz System and Synchronized Confusion-Diffusion

The inherent characteristics of chaotic systems, such as sensitivity to initial conditions and resistance to violent attacks, make them well-suited for image encryption schemes. Consequently, researchers have proposed numerous chaos-based image encryption methods. However, the simplicity of some classical chaotic system structures introduces vulnerabilities in existing schemes. These vulnerabilities often manifest as uneven encryption results and incomplete concealment of original image information, making the systems susceptible to password analysis attacks. To address these limitations, this paper introduces an improved Lorenz system, termed 'ImproLorenz,' characterized by a larger Lyapunov exponent for enhanced performance. The ImproLorenz chaotic system is iteratively solved using the modified Kutta format of the fourth-order Runge-Kutta method. Furthermore, current medical image encryption algorithms typically handle one image at a time. This approach proves inefficient for medical instruments that generate multiple images per examination. Additionally, the traditional separate implementation of confusion and diffusion operations in image encryption systems exposes vulnerabilities, as each step can be individually targeted. Therefore, leveraging the ImproLorenz chaotic system, this paper proposes a batch medical image encryption system employing synchronized confusion-diffusion. The system first establishes the initial value of the chaotic system and utilizes plaintext information to generate a key stream iteratively through the ImproLorenz system. Subsequently, multiple two-dimensional medical images are transformed into a three-dimensional Latin Cube image matrix. This matrix, combined with the password stream, undergoes non-redundant confusion to obfuscate the image data effectively. To ensure thorough encryption, the ciphertext undergoes two rounds of iterative encryption. Experimental results confirm the efficacy of the proposed image encryption scheme. The scheme exhibits high information entropy, closely approaching the theoretical value, indicating strong randomness in the encrypted data. Moreover, the scheme demonstrates robust resistance against various attacks, coupled with fast encryption speed and high security, making it suitable for securing sensitive medical image data.