A novel memristor-coupled 3D hyperchaotic system and its application in image encryption

Abstract In recent years, chaotic maps based on discrete memristors have attracted increasing research interest. However, most existing memristive chaotic maps exhibit relatively small Lyapunov exponents, whereas high values are essential for enhancing security applications. In this paper, we propose a novel three-dimensional memristive Hénon map (3D-MHM) by coupling discrete memristors with the classical Hénon map. The proposed system exhibits larger Lyapunov exponents, with the maximum value approaching 9, and a more continuous hyperchaotic range, indicating improved chaotic behavior and richer dynamic features. Furthermore, results from the National Institute of Standards and Technology tests demonstrate that the chaotic sequences generated by the 3D-MHM possess excellent randomness, with the pass rate of each test exceeding 97%. And we construct a hardware platform and successfully implement the attractors generated by the 3D-MHM. Based on the 3D-MHM, we propose a novel encryption algorithm. Experimental results and security analysis show that the encryption algorithm achieves strong performance and high efficiency. The proposed encryption algorithm can get good scores, such as correlation coefficients (<0.009) and information entropy (7.9998).