一类五维忆阻混沌系统分析及其在图像加密的应用

Analysis of a class of five-dimensional memristive chaotic systems and application in image encryption

摘要

随着数字网络中信息流的快速传输,图像作为关键信息载体,在传输过程中面临着严峻的安全威胁。本文通过在一个四维混沌系统中引入双曲正切忆阻器模型,构建一个新型的五维忆阻混沌系统。首先,通过吸引子相图、耗散性、平衡点稳定性、分岔图和Lyapunov指数等指标系统地分析该系统的动力学特性,结果表明该系统表现出丰富的超混沌行为。其次,将该混沌系统与图像加密算法相结合,设计一种基于置乱-扩散架构的新型加密方案。最后,对该加密算法进行全面的安全性分析。实验结果表明,该算法能够有效抵御多种攻击,具有较高的安全性。

Abstract

With the rapid transmission of information flow in digital networks, images, as key information carriers, face severe security threats during transmission. This paper introduces a hyperbolic tangent memristor model into a four-dimensional chaotic system to construct a novel five-dimensional memristor chaotic system. Firstly, the dynamical characteristics of the system are systematically analyzed from aspects such as attractor phase diagrams, dissipation, stability of equilibrium points, bifurcation diagrams, and Lyapunov exponents. The research results show that the system exhibits rich hyperchaotic behaviors. Subsequently, the chaotic system is combined with an image encryption algorithm to design a new encryption scheme based on the scrambling-diffusion architecture. Finally, a comprehensive security analysis of the encryption algorithm is conducted. The experimental results demonstrate that the algorithm can effectively resist various attacks and has high security.

关键词

忆阻器 / 混沌系统 / 图像加密 / 安全性分析

Key words

memristor / chaotic system / image encryption / security analysis

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基金资助

河南省高等学校重点科研项目计划支持(24B110007)

河南省研究生教育改革与质量提升工程项目(YJS2025KC03)

河南省研究生教育改革与质量提升工程项目(YJS2026AL002)

华北水利水电大学研究生创新课题(NCWUYC-202416088)

华北水利水电大学教改项目(2024XJGXM071)