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

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.