基于m-序列的本原σ-LFSR序列构造  

Construction of primitive tr-LFSR sequences from m-sequences

作　　者：刘向辉[1] 韩文报[1] 曾光[1] 

机构地区：[1]解放军信息工程大学信息研究系,郑州450002

出　　处：《四川大学学报（自然科学版）》2009年第6期1645-1649,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家863高技术研究发展计划(2006AA01Z425);国家自然科学基金(90704003)

摘　　要：σ-LFSR是一基于字的LFSR模型,它能够充分利用现代CPU的特点,具有结构简单、适合软件快速实现的特点.在实际应用中,本原σ-LFSR最有价值,因此它的构造具有重要意义.本文首先考察了基于字的本原LFSR的距离向量,得到了它的若干性质,给出了一个距离向量为本原LFSR的充要条件;然后对本原σ-LFSR的距离向量进行了研究,利用基判别定理给出了它的部分性质,并以此为基础得到了一个利用m-序列构造本原σ-LFSR序列的搜索算法.最后对搜索算法编程实现,得到了有限域F_(2~3)上所有2级本原σ-LFSR的距离向量.Abstract：σ-LFSR is a kind of word-oriented LFSR with high efficiency and good cryptographic properties, especially its software implementation is sequences are of the most valuable, so its construction is very important. Firstly, by studying the interval vectors of primitive LFSR based on word, a sufficient and necessary condition for one interval vector being a obtained. At last, programming of the search algorithm is realized and all the interval vectors of 2 stages primitiveσ-LFSR on F_(2~3) are given.σ-LFSR is a kind of word-oriented LFSR with high efficiency and good cryptographic properties, especially its software implementation is efficient for modern processors.But in practicality,primitive σ-LFSR sequences are of the most valuable,so its construction is very important.Firstly,by studying the interval vectors of primitive LFSR based on word,a sufficient and necessary condition for one interval vector being a primitive LFSR is given.Then,the interval vectors of primitive σ-LFSR are studied,some properties of primitive σ-LFSR are given and a search algorithm constructing primitive σ-LFSR sequences from m-sequences is obtained.At last,programming of the search algorithm is realized and all the interval vectors of 2 stages primitive σ-LFSR on F_2~3 are given.

关 键 词：序列 本原 LFSR 距离向量 CRYPTOGRAPHIC properties necessary condition 搜索算法 search algorithm high efficiency implementation especially 部分性质 特点 实际应用 判别定理 快速实现 结构简单 构造 充要条件 编程实现 

分 类 号：N55[自然科学总论]