| 周期二元序列线性复杂度及其最小错误之间的关系 |
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| 引用本文： | 李月清. 周期二元序列线性复杂度及其最小错误之间的关系[J]. 首都师范大学学报(自然科学版), 2013, 34(4): 5-8,18 |
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| 作者姓名： | 李月清 |
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| 作者单位： | 北京工业职业技术学院,北京,100042 |
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| 摘 要： | 密码学意义上强的序列不仅应该具有足够高的线性复杂度,而且少量比特发生变化时不会引起线性复杂度的急剧下降,即线性复杂度必须稳定.本文通过分析x2npm-1在有限域F2上的不可约分解式,给出了2npm-周期二元序列线性复杂度LC(S)的表达式,研究了使得2npm-周期序列线性复杂度下降的条件以及使得线性复杂度下降所必须最少要改变的比特数(min_error(S))的上界,这里p为奇素数,2是一个模p2的本原根.
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| 关 键 词： | 流密码 周期序列 线性复杂度 最小错误 |
A Relationship Between the Linear Complexity and the Min_error for Periodic Binary Sequences |
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| Li Yueqing. A Relationship Between the Linear Complexity and the Min_error for Periodic Binary Sequences[J]. Journal of Capital Normal University(Natural Science Edition), 2013, 34(4): 5-8,18 |
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| Authors: | Li Yueqing |
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| Affiliation: | Li Yueqing(Beijing Polytechnic College,Beijing 100042) |
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| Abstract: | Cryptographically strong sequences should not only have a large linear complexity,but also the change of a few terms should not cause a significant decrease of the linear complexity.This requirement leads to the theory of the stability of linear complexity.Based on the analysis of the canonical factorization of x2npm-1 in F2,this correspondence gives the expression of the linear complexity for 2npm-periodic binary sequences,shows the condition to make the linear complexity to decrease and the upper bound on min_error（S）,that is the number of bits that have to be changed to decrease the linear complexity,where p is an odd prime and 2 is a primitive root modulo p2. |
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| Keywords: | stream cipher periodic sequence linear complexity min_error(S) |
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