关于伪随机k元序列的研究

发布时间：2018-03-12 11:32

本文选题：伪随机k元序列　切入点：割圆类　出处：《西北大学》2017年硕士论文　论文类型：学位论文

【摘要】：伪随机序列在GPS跟踪系统和雷达监测等方面具有广泛的应用,其构造方法及随机性分析是伪随机序列理论研究的主要问题.一致分布测度、相关测度以及碰撞与雪崩效应是作为判断伪随机序列好坏的关键指标,具有重要的研究意义.本文通过广义割圆类构造大族长度为pq的伪随机k元序列,并证明其具有很好的伪随机性.首先,基于Whiteman广义割圆类构造了一大族长度为pq的伪随机k元序列.综合运用中国剩余定理、三角恒等式、指数和、特征和,研究了该序列的一致分布测度、2阶与3阶相关测度以及碰撞与雪崩效应.其次,基于Ding-Helleseth广义割圆类构造了一大族长度为pq的伪随机k元序列,并证明其具有很好的伪随机性.最后,通过对模pq剩余类环Z_(pq)进行分割,进而结合离散对数的方法,构造了一大族长度为pq的伪随机k元序列,并证明其具有很好的伪随机性.
[Abstract]:Pseudo random sequence is widely used in the GPS tracking system and radar monitoring, its construction method and stochastic analysis is the main problem of pseudo random sequence theory. Uniform distribution measure, correlation measure and collision with the avalanche effect as a key indicator to judge the pseudo-random sequence of good and bad, has important significance in this paper. The generalized cyclotomic class structure: length of pseudorandom sequence PQ K yuan, and prove that it has good pseudo randomness. Firstly, Whiteman generalized cyclotomic class to construct a family of length pseudo-random K sequence based on PQ. The integrated use of China remainder theorem, trigonometric identities, index and characteristics and, the uniform distribution of measure of the sequence, 2 order and 3 order correlation measure and collision with the avalanche effect. Secondly, Ding-Helleseth generalized cyclotomic class to construct a family of length pseudo-random K sequence based on pq, It is proved that it has a good pseudo randomness. Finally, by partitioning the residue class ring Z_ (PQ) of modular PQ and combining discrete logarithm method, a large family of pseudorandom K element sequences with length PQ is constructed, and it is proved that it has good pseudo randomness.

【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP309

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