An Efficient Batch Medical Image Encryption System Based on Improved Lorenz System and Synchronous Scrambling-Diffusion

Chaotic systems have become a popular choice for image encryption due to their desirable properties such as sensitivity to initial conditions and system parameters. While numerous chaotic-based image encryption schemes have been proposed, some suffer from vulnerabilities such as incomplete ciphertext information hiding, leaving them susceptible to attacks. This paper introduces an improved Lorenz system (ImproLorenz) with enhanced ergodicity characterized by a larger Lyapunov exponent, leading to better performance. The ImproLorenz system is iteratively solved using the deformed Kutta format of the fourth-order Runge-Kutta method.

Traditional medical image encryption algorithms often process one image at a time, proving inefficient for medical instruments that generate multiple images per examination. Moreover, the separation of scrambling and diffusion operations in conventional image encryption systems introduces security risks. To address these limitations, this paper proposes a novel batch medical image encryption system based on the ImproLorenz chaotic system and a synchronous scrambling-diffusion mechanism.

The system initially sets the chaotic system's initial value and generates the keystream iteratively using the ImproLorenz system based on plaintext information. Multiple two-dimensional medical images are then reshaped into a three-dimensional Latin Cube. The keystream is used to encrypt the plaintext within the Latin Cube without repetition, effectively concealing the image data. This process results in the ciphertext image.

Experimental results confirm the effectiveness of the proposed image encryption scheme. It exhibits high information entropy, closely approaching the theoretical value, signifying a high level of randomness in the encrypted images. Additionally, the system demonstrates strong resilience against various attacks, fast encryption speed, and high security. The synchronous scrambling-diffusion process ensures that both scrambling and diffusion operations are performed simultaneously, enhancing the system's resistance against cryptanalysis. The use of the Latin Cube structure allows for the efficient encryption of multiple medical images, reducing the overall encryption time.