计算Arnold变换周期的新算法

Arnold变换的周期在图像置乱、图像水印和信息隐藏中具有重要的应用。为了更有效地进行图像置乱等操作，同时，为了进行Arnold变换在图像置乱等安全性的研究，需要更深入和全面地研究Arnold变换的周期及其规律性。为寻找更快地计算Arnold变换周期的新算法，应用迭代Arnold变换矩阵与Fibonaeei序列之间的关系，建立了通过Fihonaeci数特征计算Amdd周期的定理。根据该定理，提出了快速计算Arnold变换周期的新算法。实验结果表明，新算法与原算法相比在计算Arnold变换周期方面，速度有了很大提高。因此，新算法适用于快速计算Arnold变换的周期和用于图像置乱等操作。另一方面，所建立的定理在理论上也是有价值的。

A New Algorithm for Calculating Period of Arnold Transformation

The period of Arnold transformation has some important applications in image scrambling,watermarking and information covering.In order to process image scrambling etc.more efficiently,meanwhile,to research the security of image scrambling using Arnold transformation,the period and its rules need to be studied deeply.The aim of this paper is to find new fast algorithm computing period of Arnold transformation.Using the relationship between iterative Arnold transformation matrix and Fibonacci sequence,a theorem for finding period of Arnold transformation matrix from the characteristics of Fibonacci numbers is established.According to this theorem,a new algorithm for fast computing the period of Arnold transformation is proposed.The results of experiments show that the new algorithm for calculating the period is much faster than old algorithms.Hence,the new algorithm is very useful for fast computing periods of Arnold transformations.On the other hand,the established theorem is valuable in theory.