An Improved Lorenz System Based Batch Medical Image Encryption Scheme with Synchronous Permutation-Diffusion

The characteristics of chaotic systems, such as sensitivity to initial values and resistance to brute force attacks, match the requirements of image encryption schemes. Therefore, scholars and experts have proposed many image encryption schemes based on chaos. 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, making it easy for attackers to crack the system through password analysis. Therefore, this paper proposes an improved Lorenz system (ImproLorenz), which has a larger Lyapunov exponent and better performance. The deformed Kutta format of the fourth-order Runge-Kutta method is used to iteratively solve the ImproLorenz chaotic system.

Most medical image encryption algorithms 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 increases time costs. In traditional image encryption systems, permutation-diffusion operations are usually divided into two basic separable or independent steps, which are vulnerable to attack. Therefore, based on the ImproLorenz chaotic system, this paper proposes a batch medical image encryption system with synchronous permutation-diffusion.

First, the initial values of the chaotic system are set, and the key stream is iteratively generated with the help of the ImproLorenz chaotic system and some plaintext information. Then, multiple two-dimensional medical images are reshaped into a three-dimensional Latin Cube, combined with the key stream, and the plaintext is encrypted non-repetitively to hide the image data. Finally, the ciphertext image can be obtained. The experimental results show that the proposed image encryption scheme is effective, with high information entropy value, closer to the theoretical value, and strong resistance to attacks, fast encryption speed, and high security.