一种改进Lorenz混沌系统构造及其加密应用  

Application of an Improved Lorenz Chaotic System and in Image Encryption

作　　者：官国荣 吴成茂[1] 贾倩[2] 

机构地区：[1]西安邮电大学电子工程学院,西安710121 [2]陕西凌云电器集团有限公司设计所,陕西宝鸡721006

出　　处：《小型微型计算机系统》2015年第4期830-835,共6页Journal of Chinese Computer Systems

基　　金：国家自然科学基金重点项目(90607008)资助;国家自然科学基金项目(61073106)资助;陕西省教育厅自然科学专项基金项目(2013JK1129)资助

摘　　要：Lorenz映射是一种被广泛研究和应用的典型混沌系统之一,但其混沌特征不能完全满足高安全性的图像加密需要,为此,提出一种改进Lorenz混沌映射构造法并将其用于图像信息安全保护.针对一种含有指数函数的改进Lorenz混沌映射存在计算溢出的不足,本文首先将含有指数函数项的改进Lorenz混沌映射修改为含有单变元二次平方项的一种新的改进Lorenz混沌映射;其次采用微分动力系统方法研究其动力学特性并证实本文改进Lorenz混沌映射具有最好的混沌特性,能够产生更加复杂的混沌吸引子;最后将改进的Lorenz混沌映射产生具有良好随机特性的离散序列用于图像的置乱和扩散加密.通过对黑白二值图像和灰度图像的加密结果相关性分析、共生矩阵指标分析和密钥敏感性能测试表明,本文所构造的一种改进的Lorenz混沌映射是有效的且能获得更大的正Lyapunov指数,同时图像加密结果的安全性有了显著的提高.Lorenz mapping is one of the typical chaotic system has been widely studied and applied,but it＇s character of chaos can＇ t fully meet the image of high security encryption required,therefore,this paper proposes an improved Lorenz chaotic mapping method and is used for the safety protection of image information. To solve the problem that a chaotic system with exponential function map- ping calculating overflow, Firstly, make it＇s exponential function change to a single variable two times square, that can construct a new and improved Lorenz chaos mapping; Secondly, study its dynamics using the method of differential dynamic system, and Prove that the improved Lorenz chaotic map has the best of chaotic characteristics, at the same time can generate chaotic attractor more complex ; Fi- nally, the improved Lorenz chaotic mapping can generate a discrete sequence with good randomness, and for image scrambling and dif- fusion encryption. Analyze the results of the black and white two value image and the gray image encryption, by using Correlation a- nalysis.co-occurrence matrix analysis and key sensitivity, Simulation result prove the improved Lorenz chaotic map constructed in this paper is effective and can obtain more positive Lyapunov exponent, At the same time, security of image encryption results have im- proved significantly.

关 键 词：LORENZ映射 LYAPUNOV指数 图像加密 相关性分析 共生矩阵 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]