无理数序列的似混沌特性及其在加密中的应用  

Chaos-like characteristics of irrational number series and its application to image encryption

作　　者：王青[1] 陈婷[1] 李锋[1] 

机构地区：[1]复旦大学电子工程系,上海200433

出　　处：《计算机工程与应用》2009年第18期85-88,93,共5页Computer Engineering and Applications

摘　　要：将已提出的π序列定义和分析方法推广到无理数领域,引出了无理数序列,并以常用的无理数根号2、e为例,对无理数序列的自相关、功率谱、相空间、关联维数、最大Lyapunov指数和主分量等6个方面进行深入分析。结果表明这些无理数序列与混沌序列具有相似的特性。然后将无理数序列应用到图像加密领域,取得了很好的图像加密效果。Irrational number series is proposed in this paper by extending the definition and analysis method of pi series to irrational numbers.This paper analyzes irrational number series of square root of 2 and e in six aspects involving autocorrelation function,Power Spectral Density（PSD）,phase space construction,correlation dimension,Principal Component Analysis（PCA） and maximal Lyapunov exponent.The results verify the chaos-like characteristics of irrational number series.Finally this paper applies the irrational number series to image encryption and gets pleasant encryption effects.

关 键 词：无理数序列 混沌序列 相空间重构 主分量分析 LYAPUNOV指数 图像加密 

分 类 号：TN911.73[电子电信—通信与信息系统]