求解本原多项式的快速算法  

Quick Algorithm for Searching Primitive Polynomial

作　　者：郭鑫[1] 陈克非[1] 

机构地区：[1]上海交通大学计算机科学与工程系,上海200240

出　　处：《计算机工程》2008年第15期146-147,189,共3页Computer Engineering

基　　金：国家自然科学基金资助项目(60573030)

摘　　要：本原元和本原多项式是有限域理论中的2个重要的概念。本原元的求解问题是解决实际密码序列问题的前提条件,而本原元的求解问题又可以归结为本原多项式的求解问题。该文结合求解最小多项式的方法给出一个在二元有限域上本原多项式的求解算法,在求解过程中同时给出了相应的最小多项式,并给出了算法相应的效能分析。Primitive elements and primitive polynomial play very important roles in the theory of the finite field. It is the premise of solving the problem about code sequences and searching the primitive elements can come down to searching primitive polynomial. This paper gives a new algorithm for searching primitive polynomials in the binary field making use of the algorithm for searching the minimal polynomial, and also gives out the minimal polynomial in the searching process. It shows the efficiency analysis of the algorithm.

关 键 词：有限域 本原元 本原多项式 最小多项式 陪集 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]