Multistability, chaos and hyperchaos in a novel 3D discrete memristive system: microcontroller implementation and cryptography

Abstract Discrete nonlinear systems involving memristors have been extensively studied in recent years. In this work, we combine the nonlinearity of a discrete memristor with a sinusoidal transformation scheme to construct a new 3D discrete hyperchaotic circuit, which is useful for image encryption. Firstly, we perform a dynamical analysis of the proposed system. Using analytical and numerical tools, we find that the model exhibits rich and complex dynamics, including fixed-point planes, hidden attractors, hyperchaos, periodicity, and multistability. To demonstrate its practical implementation, the proposed oscillator is integrated into a microcontroller-based laboratory setup, and the experimental results closely match the numerical findings. Secondly, hyperchaotic sequences generated by the new model are used to build a simple 8 × 8 S-box for secure image encryption. The hyperchaotic sequences are first used to shuffle the columns and rows of the original image, which is then substituted using the 8 × 8 substitution box and finally encrypted through nonlinear diffusion. To validate the performance of our protocol, we conduct standard security analyses, including correlation coefficient evaluation, pixel change rate, information entropy, time complexity, and key space analysis. The results are in perfect agreement with those in the literature.