基于m-序列的本原σ-LFSR序列构造

sigma-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sigma-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sigma-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sigma-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F2^3上所有2级本原sigma-LFSR的距离向量。

Construction of Primitive sigma-LFSR Sequences from m-sequences

sigma-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 sigma-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 sigma-LFSR are studied, some properties of primitive sigma-LFSR are given and a search algorithm constructing primitive sigma-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 sigma-LFSR on F2^3 are given.