New Discrete Memristive Hyperchaotic Map: Modeling, Dynamic Analysis, and Application in Image Encryption

Fei Yu¹Yiya Wu¹Xuqi Wang¹Ting He¹Shankou Zhang¹Jie Jin^2*

• ¹Changsha University of Science and Technology, Changsha, Anhui Province, China
• ²Changsha Medical University, Changsha, Hunan Province, China

With the rapid development of information technology, the demand for ensuring data security and privacy protection has become increasingly urgent. The purpose of this study is to address the limitations of existing image encryption methods and develop a more secure and efficient image encryption scheme. To achieve this, we adopt a research method that involves constructing a new type of discrete memristor hyperchaotic map by coupling an upgraded cosine discrete memristor with the Cubic map, and then conducting in-depth analysis of the system's dynamic characteristics using phase diagrams, Lyapunov exponential spectra, and bifurcation diagrams to confirm its ability to reach a hyperchaotic state. Based on this hyperchaotic map, we propose a new image encryption scheme, generating high-quality chaotic sequences through its excellent chaotic characteristics to effectively scramble and diffuse image data, and also introducing a novel forward and reverse diffusion strategy in the diffusion process to enhance encryption efficiency. Through experiments on various images, we verify the algorithm's effectiveness in improving encryption strength, reducing information leakage risks, and ensuring data security. Finally, the results of keyspace analysis, histogram analysis, correlation analysis, and information entropy demonstrate that the scheme has high security and practicability, along with good application prospects and practical value.