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| 周期二元序列的线性复杂度及其稳定性分析 | |
| 引用本文： | 牛志华,李乃成,肖国镇. 周期二元序列的线性复杂度及其稳定性分析[J]. 工程数学学报, 2006, 23(5): 901-904 |
| 作者姓名： | 牛志华 李乃成 肖国镇 |
| 作者单位： | 1. 上海大学计算机工程与科学学院,上海,200072;信息安全国家重点实验室(中国科学院研究生院),北京,100080 2. 西安交通大学理学院,西安,710049 3. 西安电子科技大学综合业务网国家重点实验室,西安,710071 |
| 摘 要： | 密码学意义上强的序列不仅应该具有高的线性复杂度而且其线性复杂度必须稳定,k-错线性复杂度用来反应线性复杂度的稳定性。本文基于x~(p~(m_2~n))-1在GF(2)上具有明确的分解式,研究了p~(m_2~n)-周期二元序列的线性复杂度和k-错线性复杂度之间的关系,然后说明了同时使得线性复杂度和k-错线性复杂度都达到最大值的p~(m_2~n)-周期二元序列是存在的。这里p是一个奇素数,2是模p~2的本原根。 |
| 关 键 词： | 流密码 周期序列 线性复杂度 k-错线性复杂度 |
| 文章编号： | 1005-3085(2006)05-0901-04 |
| 收稿时间： | 2004-10-11 |
| 修稿时间： | 2004-10-15 |
Analysis of the Linear Complexity and Its Stability for Periodic Binary Sequences |
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| NIU Zhi-hua,LI Nai-cheng,XIAO Guo-zhen. Analysis of the Linear Complexity and Its Stability for Periodic Binary Sequences[J]. Chinese Journal of Engineering Mathematics, 2006, 23(5): 901-904 | |
| Authors: | NIU Zhi-hua LI Nai-cheng XIAO Guo-zhen |
| Affiliation: | 1- School of Computer Engineering and Science, Shanghai University, Shanghai 200072; 2- State Key Laboratory of Information Security (Graduate School of Chinese Academy of Sciences |
| Abstract: | Cryptographically strong sequences should not only have a high linear complexity,but also altering a few terms should not cause a significant decline of the linear complexity.This requirement leads to the concept of the k-error linear complexity of periodic sequence. Based on the explicit factorization of x~((p~m)(2~n))-1 over GF(2),this correspondence focuses on the relationship between the linear complexity and the k-error linear complexity of the p~m2~n-periodic binary sequences,where p is an odd prime number,2 is a primitive root mod- ulo p~2.Then we establish the existence of p~m2~n-periodic sequences which simultaneously achieve the maximum value of the linear complexity and the k-error linear complexity. |
| Keywords: | stream ciphers periodic sequences linear complexity k-Error linear complexity |
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