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

• 网络、通信、安全 • Previous Articles     Next Articles

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

WANG Qing,CHEN Ting,LI Feng   

  1. 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   

  1. 复旦大学 电子工程系,上海 200433
  • 通讯作者: 王 青

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