Kaprekar序列的似混沌特性及其在图像加密中的应用  

Chaos-like characteristics of Kaprekar series and its application in image encryption

作　　者：王圣[1] 商慧亮[1] 韩贵丞[1] 李锋[1] 

机构地区：[1]复旦大学电子工程系,上海200433

出　　处：《太赫兹科学与电子信息学报》2013年第1期125-130,共6页Journal of Terahertz Science and Electronic Information Technology

摘　　要：为获得采用整型运算的似混沌序列,基于Kaprekar变换并利用Kaprekar常数的数学性质,构造一种新的时间序列——Kaprekar序列。利用时间序列的分析方法对Kaprekar序列进行功率谱特性、相空间重构、最大Lyapunov指数和主分量等方面的分析,与经典Logistic序列进行比较,得到Kaprekar序列与混沌序列的关系。结果表明,Kaprekar序列具有似混沌特性,并有完全采用整型计算的优点。将Kaprekar序列应用于图像加密中,取得了很好的实验结果。A kind of new time series named Kaprckar series are created based on Kaprekar operation and Kaprckar constant to obtain chaos-like series with integer operation. Several analysis methods for time series are applied to research their characteristics, including Power Spectral Density（PSD）, phase space construction, maximal Lyapunov exponents and Principal Component Analysis（PCA） and so on. Through cyber-simulation and the comparison with Logistic series, the chaos-like characteristics of Kaprekar series are validated. Kaprekar series are then applied to image encryption, and good results are obtained in image encryption experiments.

关 键 词：Kaprekar序列 似混沌特性 LYAPUNOV指数 主分量分析 图像加密 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]