A 3D Memristive Cubic Map With Dual Discrete Memristors: Design, Implementation, and Application in Image Encryption

Abstract

Discrete chaotic systems based on memristors exhibit excellent dynamical properties and are more straightforward to implement in hardware, making them highly suitable for generating cryptographic keystreams. However, most existing memristor-based chaotic systems rely on a single memristor. This paper introduces a novel discrete chaotic system employing dual memristors, named the 3D memristive cubic map with dual discrete memristors (3D-MCM). The 3D-MCM system demonstrates richer and more intricate dynamical behaviors compared to its single-memristor counterparts, as verified through bifurcation diagrams, Lyapunov exponent spectra, and complexity analyses. Notably, the system exhibits coexisting attractors, substantially enhancing its dynamical complexity. Hardware implementation of the 3D-MCM attractors confirms its feasibility for industrial applications. To illustrate the system’s potential in encryption tasks, this study integrates the quaternary-based permutation and dynamic emanating diffusion (QPDED-IE) scheme with the 3D-MCM for image encryption. Experimental results demonstrate that the QPDED-IE scheme based on the 3D-MCM exhibits strong diffusion and confusion properties, effectively resisting cryptanalytic attacks.