具有良好线性复杂度和错误线性复杂度性质的密码周期序列的设计与分析

项目名称： 具有良好线性复杂度和错误线性复杂度性质的密码周期序列的设计与分析

项目编号： No.U1304604

项目类型： 联合基金项目

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： 常祖领

作者单位： 郑州大学

项目金额： 30万元

中文摘要： 本项目将充分利用有限域理论、数论、组合设计、频谱理论、布尔函数、代数编码理论等工具对二元$2^n$周期序列进行深入系统的研究，分析这种序列的密码学性质；研究二元周期序列的k-错线性复杂度的分布、期望及其随k 增大而降低的规律；研究二元周期序列的错误线性复杂度谱的结构、严格点的性质；研究二元周期序列的严格错误序列的计数及算法；研究具有良好线性复杂度和错误线性复杂度的序列的构造；研究二元周期序列的自相关性质及其与错误线性复杂度之间的关系；研究有限域上序列的k-错线性复杂度的分布；进一步研究已得结果在流密码的分析与设计以及在其它多个领域如重根循环码及码分多址通信系统中的应用。其成果将对流密码理论的研究产生一定的影响，并将广泛应用于安全密码系统的分析和设计以及通信领域等多个领域中。

中文关键词： 二元周期序列；分圆序列；线性复杂度；错误线性复杂度；相关函数

英文摘要： This project will deeply and systematically study the cryptographic binary $2^n$-periodic sequences by using the tools including finite fields, number theory, combinatorics and designs, spectrum theory, Boolean functions theory, algebraic coding theory, etc. We will analyze the cryptographic properties of binary $2^n$-periodic sequences, the distribution and the expectation of the k-error linear complexity of binary $2^n$-periodic sequences and the falling rules of k-error linear complexity. We will study the construction of the error linear complexity spectrum and the properties of critical points in it. We will study the enumeration and algorithms about the critical error sequences of binary $2^n$-periodic sequences. We will study the construction of periodic sequences with large linear complexity and error linear complexity. We will study the relations between auto-correlation and error linear complexity of binary sequences. We will study the distribution of k-error linear complexity of sequences over general finite fields. We will also study the application of our results in the analysis and designs of stream ciphers and other domains such as repeated-root cyclic codes and CDMA(Code Division Multiple Access) communication systems. The results of this project will take some influence in the study of stream ci

英文关键词： binary periodic sequences；cyclotomic sequences；linear complexity；error linear complexity；correlation function