Period Distribution of Generalized Discrete Arnold Cat Map for N = pe
Period Distribution of Generalized Discrete Arnold Cat Map for N = pe
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DOI：
10.1109/tit.2011.2171534
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发表时间：
2012-01-01
影响因子：
2.5
通讯作者：
Xiang, Tao
中科院分区：
文献类型：
--
作者：
Chen, Fei;Wong, Kwok-Wo;Xiang, Tao
本文分析了伽罗瓦环（Z(pe), +, x）上广义离散cat映射的周期分布，其中p > 3为素数。该映射生成的序列被建模为二维LFSR序列。采用生成函数法和Hensel提升法，分析得到了详细的周期分布。我们的研究结果不仅刻画了cat图的周期分布，为各种应用提供了见解，而且还展示了处理伽罗瓦环中多项式周期的一些方法。
In this paper, we analyze the period distribution of the generalized discrete cat map over the Galois ring (Z(pe), +, x) where p > 3 is a prime. The sequences generated by this map are modeled as 2-dimensional LFSR sequences. Employing the generation function and the Hensel lifting approaches, full knowledge of the detail period distribution is obtained analytically. Our results not only characterize the period distribution of the cat map, which gives insights to various applications, but also demonstrate some approaches to deal with the period of a polynomial in the Galois ring.