构造de Bruijn序列方法的研究

发布时间：2018-05-17 06:20

本文选题：NFSR序列 + 伪随机性质　；参考：《郑州大学》2017年硕士论文

【摘要】：近年来,以NFSR序列作为驱动序列的序列密码体制逐渐受到密码设计者们的关注。如何构造大周期、伪随机性质良好的NFSR序列是一个热门课题。De Bruijn序列是一类非常重要的NFSR序列,具有大周期、良好的平衡性及高的线性复杂度等特性,在密码学及通信等领域中有广泛的应用。因此,deBruijn序列的构造问题一直是研究的热点。本文给出了两种新的构造de Bruijn序列的方法。第一种是优先取补法。通过直接添加前一个比特的补,得到一种直接构造deBruijn序列的方法。第二种是并圈法。对于纯轮换寄存器生成的圈,当且仅当给出的状态或其共轭状态为圈代表时进行并圈,就得到了一种基于PCR构造de Bruijn序列的方法。
[Abstract]:In recent years, the sequence cipher system with NFSR sequence as the driving sequence has gradually attracted the attention of the cryptographic designers. How to construct a NFSR sequence with large period and good pseudo random properties is a hot topic,.De Bruijn sequence is a very important class of NFSR sequences, with a large period, good balance and high linear complexity, etc. There are extensive applications in cryptography and communications. Therefore, the construction of deBruijn sequences has been a hot spot of research. In this paper, two new methods for constructing de Bruijn sequences are given. The first is the priority complement method. By adding the complement of the previous bit directly, a method of constructing the deBruijn sequence directly is obtained. The second is the method to construct the sequence directly. The loop method. For the cycles generated by the pure rotation register, when and only when the given state or its conjugate state is carried and ring on the circle, a method of constructing the de Bruijn sequence based on PCR is obtained.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN918

【参考文献】