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.
出处
《计算机工程与应用》
CSCD
北大核心
2009年第18期85-88,93,共5页
Computer Engineering and Applications
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
irrational number series
chaos series
phase space reconstruction
Principal Component Analysis（ PCA ）
Lyapunov exponent
image encryption
