A Dynamic Hill Cipher with Arnold Scrambling Technique for Medical Images Encryption

Cryptography is one of the most important branches of information security. Cryptography ensures secure communication and data privacy, and it has been increasingly applied in healthcare and related areas. As a significant cryptographic method, the Hill cipher has attracted significant attention from experts and scholars. To enhance the security of the traditional Hill cipher (THC) and expand its application in medical image encryption, a novel dynamic Hill cipher with Arnold scrambling technique (DHCAST) is proposed in this work. Unlike the THC, the proposed DHCAST uses a time-varying matrix as its secret key, which greatly increases the security of the THC, and the new DHCAST is successfully applied in medical images encryption. In addition, the new DHCAST method employs the Zeroing Neural Network (ZNN) in its decryption to find the time-varying inversion key matrix (TVIKM). In order to enhance the efficiency of the ZNN for solving the TVIKM, a new fuzzy zeroing neural network (NFZNN) model is constructed, and the convergence and robustness of the NFZNN model are validated by both theoretical analysis and experiment results. Simulation experiments show that the convergence time of the NFZNN model is about 0.05 s, while the convergence time of the traditional Zeroing Neural Network (TZNN) model is about 2 s, which means that the convergence speed of the NFZNN model is about 400 times that of the TZNN model. Moreover, the Peak Signal to Noise Ratio (PSNR) and Number of Pixel Change Rate (NPCR) of the proposed DHCAST algorithm reach 9.51 and 99.74%, respectively, which effectively validates its excellent encryption quality and attack prevention ability.