Effect of the memristor on Hopfield artificial neural networks and their application in encryption

Abstract One way to strengthen encryption algorithms against attacks is to increase of encryption keys and the level of disorder in the encryption system. This paper investigates a cosine-based memristive model W(φ) = cos(φ) by analyzing the effects of signal amplitude, frequency, and boundary conditions. The proposed memristive element exhibits strong nonlinearity and memory properties, making it suitable for chaotic applications. The memristor is incorporated into a three-cell Hopfield neural network, where it operates as a synaptic coupling element, an external radiation sensor, and a dynamic weight controller. These mechanisms generate rich chaotic dynamics, which are verified using bifurcation diagrams, Lyapunov exponents, and phase space analysis. Numerical simulations in MATLAB are experimentally validated using an ESP32 microcontroller, with chaotic signals observed on an oscilloscope. Based on the proposed Hopfield, an image encryption scheme is developed and evaluated. The encryption results demonstrate high security performance, with entropy of 7.9977, near-zero pixel correlation, NPCR of 99.64%, and PSNR of 6.77. The complete system is practically implemented using an ESP32, a Raspberry Pi, and a computer, confirming its feasibility for real-time secure communication.