一种三阶分段线性混沌系统及其在图像加密中的应用  

A third order piecewise linear chaotic system and its application in image encryption

作　　者：刘嵩 张建强[2] 邱达 刘静漪 张国平 LIU Song;ZHANG Jianqiang;QIU Da;LIU Jingyi;ZHANG Guoping(School of Advanced Materials and Mechatronic Engineering,Hubei University for Nationalities,Enshi 445000,Hubei,China;College of Physical Science and Technology,Central China Normal University,Wuhan 430079,China)

机构地区：[1]湖北民族大学新材料与机电工程学院,湖北恩施445000 [2]华中师范大学物理科学与技术学院,武汉430070

出　　处：《华中师范大学学报（自然科学版）》2023年第2期213-222,共10页Journal of Central China Normal University：Natural Sciences

基　　金：湖北省教育厅优秀青年科技创新团队项目(T201611);湖北民族大学博士基金项目(MD2020B021)。

摘　　要：基于异宿环Shilnikov定理,该文提出了一个三阶分段线性混沌系统,构建了该系统两个平衡点之间的异宿环,证明了异宿环存在的充分条件,分析了混沌吸引子的形成机理,验证了系统的可实现性.应用该系统产生混沌数据序列,构建置乱矩阵和随机扩散矩阵对图像进行加密.在MATLAB平台进行了密钥敏感性分析、相关性分析、信息熵分析和抗噪声分析等.实验结果表明:该算法有较好的加密效果与抗攻击能力.In this paper,a third order piecewise linear chaotic system based on Shilnikov theorem is proposed,and a heteroclinic loop of this system is constructed between its two equilibrium points.The existence conditions of the heteroclinic loop are proved,the mechanism underlying the formation of the chaotic attractor is analyzed,and the validity and feasibility of the system is verified.Then based on the proposed chaotic system,the chaotic data sequence is generated,and the scrambling matrix and random diffusion matrix are constructed to encrypt the image.Security analyses including key sensitivity analysis,correlation analysis of adjacent pixels,information entropy analysis and anti-noise analysis are performed in matlab.The experimental results demonstrate that the proposed image encryption scheme can resist various attacks and shows better effectiveness.

关 键 词：分段线性 异宿环 图像加密 混沌 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]