A Novel Batch Medical Image Encryption System Based on Improved Lorenz Chaotic System with Synchronous Permutation-Diffusion

The characteristics of chaotic systems align with the sensitivity and resistance to violent attacks required for image encryption schemes. Therefore, scholars have proposed many chaos-based image encryption schemes. However, due to the simplicity of some classical chaotic system structures, existing encryption schemes have problems such as uneven encryption results and incomplete hiding of original image information, which makes it easy for attackers to crack the system through password analysis. Therefore, this paper designs an improved Lorenz system (ImproLorenz), which has a larger Lyapunov exponent and better performance, and uses the fourth-order Runge-Kutta method's modified Kutta format to iteratively solve the ImproLorenz chaotic system. Most medical image encryption algorithms currently can only encrypt one medical image at a time. However, many medical instruments generate multiple medical images in one examination, and encrypting one image at a time will increase time costs. In traditional image encryption systems, the permutation-diffusion operation is usually divided into two basic separable or independent steps, which can be individually targeted and easily attacked. Therefore, based on the ImproLorenz chaotic system, this paper proposes a batch medical image encryption system with synchronous permutation-diffusion. First, set the initial value of the chaotic system and iteratively generate the keystream using the ImproLorenz chaotic system with the help of some plaintext information. Then, reshape multiple two-dimensional medical images into a three-dimensional Latin Cube image matrix, combine with the keystream, and non-repetitively confuse the plaintext to hide image data. In order to thoroughly encrypt medical images, the ciphertext is iteratively encrypted twice. Finally, the password image can be obtained. Experimental results show that the proposed image encryption scheme is effective, with a higher information entropy value closer to the theoretical value, and has strong anti-attack capabilities, fast encryption speed, and high security.