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

doi:10.3778/j.issn.1002-8331.2009.18.027

Computer Engineering and Applications ›› 2009, Vol. 45 ›› Issue (18): 85-88.DOI: 10.3778/j.issn.1002-8331.2009.18.027

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

WANG Qing,CHEN Ting,LI Feng

Department of Electronical Engineering，Fudan University，Shanghai 200433，China

Received:2008-09-25 Revised:2008-12-18 Online:2009-06-21 Published:2009-06-21
Contact: WANG Qing

无理数序列的似混沌特性及其在加密中的应用

王青,陈婷,李锋

复旦大学电子工程系，上海 200433

通讯作者: 王青

Abstract

Abstract: 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.

Key words: irrational number series, chaos series, phase space reconstruction, Principal Component Analysis（PCA）, Lyapunov exponent, image encryption

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。

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

WANG Qing,CHEN Ting,LI Feng. Chaos-like characteristics of irrational number series and its application to image encryption[J]. Computer Engineering and Applications, 2009, 45(18): 85-88.

王青,陈婷,李锋. 无理数序列的似混沌特性及其在加密中的应用[J]. 计算机工程与应用, 2009, 45(18): 85-88.

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

无理数序列的似混沌特性及其在加密中的应用

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