伽罗瓦环上几类序列的构造及其密码学性质的研究

发布时间：2018-04-16 22:34

本文选题：序列密码 + 二相序列　；参考：《合肥工业大学》2017年硕士论文

【摘要】：目前,序列的广泛应用涉及到码分多址通信、扩频通信、全球定位系统、密码学、计算、控制等领域。在所涉及的领域中,具有良好的密码学性质的序列占有着非常重要的地位,而线性复杂度和相关性是评价序列好坏的两个重要的指标。长期以来,序列构造设计的研究一直被国际社会所关注,寻找一些新的方法来构造设计出性质良好的序列以及分析其密码学性质是非常有研究价值的。本文主要对伽罗瓦环上的几类序列的构造及其相关密码学性质进行研究。主要的研究内容如下:(1)定义了一个从Zks到Zks-1×Z2s-1k上的映射Z,通过利用映射Z和伽罗瓦环Z2s上的(2s-1 +1)-常循环码构造出一类具有最小Lee距离下界的循环Z2s-1-码。(2)基于已构造的循环Z2s-1-码来构造出一类具有低相关性的2s-1相序列。(3)基于已构造的2s-1相序列,通过利用最高权位映射得到一类具有低相关性的二相序列。(4)利用伽罗瓦环上的置换,构造出伽罗瓦环Zpe上的一类新的No序列,并给出其线性复杂度的精确下界。
[Abstract]:At present, sequences are widely used in the fields of code division multiple access communication, spread spectrum communication, global positioning system, cryptography, computing, control and so on.In the fields involved, sequences with good cryptographic properties play a very important role, and linear complexity and correlation are two important indicators to evaluate the quality of sequences.For a long time, the research of sequence structure design has been paid much attention by the international community. It is very valuable to find some new methods to construct the sequence with good properties and to analyze its cryptographic properties.In this paper, the construction and cryptographic properties of several classes of sequences on Galois rings are studied.The main research contents are as follows: 1) A mapping Z from Zks to Zks-1 脳 Z2s-1k is defined. By using the mapping Z and Galois ring Z2s, a class of cyclic Z2s-1- codes with minimum Lee distance is constructed by using the mapping Z and the Galois ring Z2s.Constructed cyclic Z2s-1- codes to construct a class of 2s-1 phase sequences with low correlation.) based on the constructed 2s-1 phase sequences,By using the highest weight mapping, we obtain a class of two-phase sequences with low correlation. We use the permutation on the Galois ring to construct a new class of No sequences on the Galois ring Zpe, and give the exact lower bound of its linear complexity.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.4

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