求GF(p^m)上周期为kn的序列线性复杂度的快速算法  

Fast algorithm for determining the linear complexity of sequences over GF(p^m) with the period kn

作　　者：戴小平[1] 周建钦[1] 

机构地区：[1]安徽工业大学计算机学院,安徽马鞍山243002

出　　处：《西安电子科技大学学报》2008年第4期759-763,共5页Journal of Xidian University

基　　金：国家自然科学基金资助(60473142);安徽省教育厅自然科学基金资助(2006KJ238B)

摘　　要：提出和证明了求GF(pm)上周期为kn的序列线性复杂度和极小多项式的一个快速算法,其中p是素数,gcd(n,pm-1)=1且pm-1=kt,n,k与t均为正整数.该算法推广了陈豪提出的求GF(pm)上周期为3n的序列线性复杂度的一个快速算法,其中p是素数,gcd(n,pm-1)=1且p-1=3t,n与t均为正整数.结合一些已知的快速算法,可以快速计算GF(pm)上周期为kn的序列线性复杂度,最后给出一个具体例子.A fast algorithm is presented for determining the linear complexity and the minimal polynomial of sequences over GF（p^m） with the period kn, where p is a prime, gcd（n, p^m -1） = 1, p^m- 1 =kt, and n, k and t are integers. The algorithm presented here covers the algorithm proposed by Chen Hao for determining the linear complexity of sequences over GF（p^m） with the period 3n, where p is a prime, gcd（n, p^m- 1） = 1, p - 1 = 3t, and n and t are integers, Combining the proposed algorithm with some known algorithms, the linear complexity of sequences over GF（p^m ） with the period kn can be determined more efficiently. Finally, an example for applying this algorithm is presented.

关 键 词：密码学 周期序列 线性复杂度 极小多项式 快速算法 

分 类 号：TN918.1[电子电信—通信与信息系统] O236[电子电信—信息与通信工程]