序列的几种复杂度及其关系研究

项目名称： 序列的几种复杂度及其关系研究

项目编号： No.61309017

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 谭林

作者单位： 中国人民解放军信息工程大学

项目金额： 25万元

中文摘要： 序列的复杂度衡量是序列伪随机性研究的重要内容，线性复杂度和2-adic复杂度是序列的两个基本的复杂度指标，k-错线性复杂度和k-错2-adic复杂度反映了序列的这两种复杂度的稳定性。本项目研究序列的这四种复杂度及其相互之间的关系。具体研究内容有：序列的线性复杂度谱与k-错线性复杂度之间的关系；随机序列的k-错线性复杂度和2-adic复杂度的均值与方差；l-序列的k-错线性复杂度和m-序列的k-错2-adic复杂度。通过本项目的研究，可以更加清晰地刻画随机序列的这四种复杂度的分布规律以及它们在序列伪随机性评价上的内在联系。

中文关键词： 序列密码；谱免疫；非线性反馈移位寄存器序列；轻量级密码；MDS矩阵

英文摘要： Complexity measures for sequences are important issues in randomness assessment of keystreams. Linear complexity and 2-adic complexity are two elementary complexity of sequences.The k-error linear complexity and k-error 2-adic complexity show the stability of the two elementary complexity of sequences, respectively. The detailed research of this project is as follows: the relationship between the linear complexiy profile and k-error linear complexity; expected value of the k-error linear complexity and 2-adic complexity of random sequences; the k-error linear complexity of l-sequences and the k-error 2-adic complexity of m-sequence. The significance of this project is to chracterize the distribution properties of the four complexity of random sequences and their inner connections in randomness assessment for sequences.

英文关键词： stream ciphers；spectral immunity ；NFSR sequences ；lightweight cryptography；MDS matrices