本原-LFSR序列的迹表示及其应用
doi: 10.3724/SP.J.1146.2008.00028
Trace Representation of Primitive -LFSR Sequences and Its Application
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摘要: -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-LFSR序列具有最核心的作用。该文分析了本原-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-LFSR序列的迹表示；其次由本原-LFSR序列的迹表示，给出了一个-LFSR序列为本原的充要条件。它们为进一步研究本原-LFSR序列提供了新的工具。Abstract: -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 -LFSR sequences are of the most importance. Firstly, by the iterative relationship of the primitive -LFSR sequences and the trace function in finite fields, the explicit expression of primitive -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 -LFSR sequence is primitive or not. They provide the new tool for further research of primitive -LFSR sequences.
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