摘要
σ-LFSR是一基于字的LFSR模型,它的设计充分利用了现代CPU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。而在实际应用中,本原σ-LFSR序列具有最核心的作用。该文分析了本原σ-LFSR序列的产生条件,利用其迭代关系式和有限域的迹函数,给出了它的具体表达式,从而得到本原σ-LFSR序列的迹表示;其次由本原σ-LFSR序列的迹表示,给出了一个σ-LFSR序列为本原的充要条件。它们为进一步研究本原σ-LFSR序列提供了新的工具。
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. Firstly, by the iterative relationship of the primitive σ -LFSR sequences and the trace function in finite fields, the explicit expression of primitive σ -LFSR sequences is presented. Therefore the trace representation is gotten; then a sufficient and necessary condition is obtained due to the trace representation. It can be used to check whether a σ-LFSR sequence is primitive or not. They provide the new tool for further research of primitive σ-LFSR sequences.
出处
《电子与信息学报》
EI
CSCD
北大核心
2009年第4期942-945,共4页
Journal of Electronics & Information Technology
基金
国家863计划项目(2006AA01Z425)
国家自然科学基金(90704003资助课题
关键词
序列密码
σ-LFSR序列
迹表示
快速软件加密
Stream cipher
σ-LFSR sequences
Trace representation
Fast software encryption
