A Memristive Fully Connect Neural Network and Application of Medical Image Encryption Based on Central Diffusion Algorithm

With the continuous development of computers, communication technology, and regional medical collaboration services, the security and confidentiality of information are becoming more and more important. In order to prevent the illegal leakage of sensitive patient information, it is of great significance to study medical image encryption. In this article, a flux-controlled hyperbolic memristor model with locally active characteristics is proposed, which has rich nonlinear characteristics. The memristor parameters affect the local activity of the memristor, which is explained by mathematical analysis. Based on the traditional hopfield neural network (HNN), a memristive fully connect neural network (MFNN) containing four neurons is constructed with more complex coupling relationships between individual neurons. The memristor can be used to characterize the effect of external electromagnetic radiation on neurons. The complex dynamical behaviors of MFNN are found by numerical simulations. An equivalent circuit for the neural network is constructed to verify the accuracy of the numerical simulation. In addition, a medical image encryption scheme based on MFNN is proposed. The encryption scheme performs a bit-level permutation of the original image using a chaotic sequence randomly generated by the chaotic system. Fibonacci
$Q$
-matrix and central diffusion algorithm are used to diffuse the permutation image. Through numerical analysis, the maximum entropy of this encryption algorithm reaches 7.99, and the correlation is close to zero, which proves the resistance of the algorithm to statistical attacks. The algorithm takes only 3.9 s to encrypt an 8-bit medical image of 320 × 320 size on Windows 10 operating system. Experimental results show that the proposed encryption scheme is very secure and has good applications in medical image encryption.