摘要
σ-LFSR是一种基于字的LFSR模型,能充分利用现代CPU的特点,可很好地应用于设计适合快速软件实现的序列密码算法中。但从伪随机特性和资源利用率的角度看,实际应用的σ-LFSR序列必定是本原的。对本原σ-LF-SR序列的性质作了较深入的分析,得到了其分位序列之间是线性无关的,并指出分位序列的极小多项式实际是状态转移矩阵的特征多项式;通过引入块Hankel矩阵,给出了一个求本原σ-LFSR序列极小多项式的算法;最后给出了σ-LFSR序列为本原的充要条件。
σ-LFSR is a kind of word-oriented LFSR with high efficiency and good cryptographic properties, especially suitable for modern processors. It can be used in stream cipher for fast software implementation. But in practicality, primitive σ-LFSR sequences are of the most importance. Proposed a thorough analysis on the properties of the primitive σ-LFSR sequences. Obtained the conclusion that the coordinate sequences of a primitive σ-LFSR sequence are linear independent, and the minimal polynomial of coordinate sequences is just the character polynomial of state transfer matrix. By introducing the block Hankel matrix, an algorithm to compute the minimal polynomial of a primitive σ-LFSR sequence was offered. At last,a sufficient and necessary condition was obtained which can be used to check whether a σ-LFSR sequence is primitive or not.
出处
《计算机科学》
CSCD
北大核心
2008年第12期119-121,共3页
Computer Science
基金
国家863高技术研究发展计划资助项目(2006AA01Z425)
国家自然科学基金资助项目(90704003)
