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...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.展开更多
In this paper, we introduce a new type of feedback shift register based on words, called G-linear feedback shift register （σ-LFSR） which can make full use of the instructions of modern CPUs so that we can find good...In this paper, we introduce a new type of feedback shift register based on words, called G-linear feedback shift register （σ-LFSR） which can make full use of the instructions of modern CPUs so that we can find good σ-LFSR with simple structure and fast software implementation. After analysis, we find a class of simple σ-LFSR with maximal period and give an algorithm of searching for those σ-LFSRs. As a result, we provide a new optional fast component in the design of modern wordbased stream ciphers.展开更多
文摘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.
基金the National Natural Science Foundation of China (Grant No. 60503011)the National High-Tech Research and Development Program of China (863 Program) (Grant No. 2006AA01Z425)the National Basic Research Program of China (973 Program) (Grant No. 2007CB807902)
文摘In this paper, we introduce a new type of feedback shift register based on words, called G-linear feedback shift register （σ-LFSR） which can make full use of the instructions of modern CPUs so that we can find good σ-LFSR with simple structure and fast software implementation. After analysis, we find a class of simple σ-LFSR with maximal period and give an algorithm of searching for those σ-LFSRs. As a result, we provide a new optional fast component in the design of modern wordbased stream ciphers.
