王锦玲,
崔静静^,
郑州大学数学与统计学院 郑州 450001
基金项目:国家自然科学基金 (61772476)

详细信息

作者简介:王锦玲：女，1963年生，教授，硕士生导师，研究方向为代数学、密码学
崔静静：女，1995年生，硕士生，研究方向为代数学、密码学

通讯作者:崔静静　17335569258@163.com

中图分类号:TN918.1

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被引次数:0

出版历程

收稿日期:2020-08-04
修回日期:2020-12-09
网络出版日期:2020-12-21
刊出日期:2021-08-10

The Period and the Linear Complexity of a New Self-shrinking Control Sequence on GF(3)

Jinling WANG,
Jingjing CUI^,
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Funds:The National Natural Science Foundation of China (61772476)


摘要
摘要:自缩控(SSC)序列是一类重要的伪随机序列，而伪随机序列在通信加密、编码技术等很多领域中有着广泛的应用。在这些应用中，通常要求序列具有大周期和高的线性复杂度。为了构造出周期更大、线性复杂度更高的伪随机序列，该文基于${\rm{GF}}(3)$上的$m$-序列构造了一种新型自缩控序列模型，利用有限域理论研究了生成序列的周期和线性复杂度，得到的生成序列周期和线性复杂度大大提高，且得到生成序列线性复杂度更精确的一个上界值，从而提高了生成序列在通信加密中的防攻击能力和安全性能。
关键词:自缩控序列/
线性复杂度/
周期/
特征多项式/
m-序列
Abstract:Self-Shrinking Control (SSC) sequences are a class of important pseudo-random sequences, and pseudo-random sequences are widely used in many fields, such as communication encryption, recoding technology. In these applications, sequences are usually required to have large periods and high linear complexity. In order to construct pseudo-random sequences with higher period and higher linear complexity, a new SSC sequence model based on the m-sequence in GF (3) is constructed, the period and the linear complexity of the generated sequence are studied by using finite domain theory, this model greatly improves the period and the linear complexity of the generated sequence, and obtains a more accurate upper bound value of the linear complexity of the generated sequence. Thus, the anti-attack ability and security performance of the generated sequence in communication encryption are improved.
Key words:Self-Shrinking Control (SSC) sequence/
Linear complexity/
Period/
Characteristic polynomial/
m-sequence



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