GF(3)上新型自缩控序列的周期与线性复杂度

王锦玲; 崔静静

doi:10.11999/JEIT200676

GF(3)上新型自缩控序列的周期与线性复杂度

doi: 10.11999/JEIT200676

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。
- 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.
- Self-Shrinking Control (SSC) sequence /
- Linear complexity /
- Period /
- Characteristic polynomial /
- m-sequence

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参考文献(19)

[1]	杜小妮, 李丽, 张福军. 基于模2p ^m的欧拉商的二元序列的线性复杂度[J]. 电子与信息学报, 2019, 41(12): 3000–3005. doi: 10.11999/JEIT190071 DU Xiaoni, LI Li, and ZHANG Fujun. Linear complexity of binary sequences derived from euler quotients modulo 2p ^m[J]. Journal of Electronics &Information Technology, 2019, 41(12): 3000–3005. doi: 10.11999/JEIT190071
[2]	王艳, 薛改娜, 李顺波, 等. 一类新的周期为2p ^m的q阶二元广义分圆序列的线性复杂度[J]. 电子与信息学报, 2019, 41(9): 2151–2155. doi: 10.11999/JEIT180884 WANG Yan, XUE Gaina, LI Shunbo, et al. The linear complexity of a new class of generalized cyclotomic sequence of order q with period 2p ^m[J]. Journal of Electronics &Information Technology, 2019, 41(9): 2151–2155. doi: 10.11999/JEIT180884
[3]	YANG Bo, DU Tianqi, and XIAO Zibi. Linear complexity of generalized cyclotomic binary sequences of period pq[J]. Journal.of Mathematics, 2020, 40(2): 139–148. doi: 10.13548/j.sxzz.2020.02.004
[4]	李瑞芳, 柯品惠. 一类新的周期为2pq的二元广义分圆序列的线性复杂度[J]. 电子与信息学报, 2014, 36(3): 650–654. doi: 10.3724/SP.J.1146.2013.00751 LI Ruifang and KE Pinhui. The linear complexity of a new class of generalized cyclotomic sequence with period 2pq[J]. Journal of Electronics &Information Technology, 2014, 36(3): 650–654. doi: 10.3724/SP.J.1146.2013.00751
[5]	杜小妮, 赵丽萍, 王莲花. Z₄上周期为2p²的四元广义分圆序列的线性复杂度[J]. 电子与信息学报, 2018, 40(12): 2992–2997. doi: 10.11999/JEIT180189 DU Xiaoni, ZHAO Liping, and WANG Lianhua. Linear complexity of quaternary sequences over Z₄ derived from generalized cyclotomic classes modulo 2p²[J]. Journal of Electronics &Information Technology, 2018, 40(12): 2992–2997. doi: 10.11999/JEIT180189
[6]	仲燕, 张胜元, 柯品惠. 一类新的周期为2p ^m的四元广义分圆序列的线性复杂度研究[J]. 福建师范大学学报: 自然科学版, 2020, 36(1): 7–11. doi: 10.12046/j.issn.1000-5277.2020.01.002 ZHONG Yan, ZHANG Shengyuan, and KE Pinhui. Research on linear complexity of a new class of quaternary generalized cyclotomic sequence with period 2p ^m[J]. Journal of Fujian Normal University:Natural Science Edition, 2020, 36(1): 7–11. doi: 10.12046/j.issn.1000-5277.2020.01.002
[7]	陈智雄, 吴晨煌. 关于二元割圆序列的k-错线性复杂度[J]. 通信学报, 2019, 40(2): 197–206. doi: 10.11959/j.issn.1000-436x.2019034 CHEN Zhixiong and WU Chenhuang. k-error linear complexity of binary cyclotomic generators[J]. Journal on Communications, 2019, 40(2): 197–206. doi: 10.11959/j.issn.1000-436x.2019034
[8]	刘龙飞, 杨晓元, 陈海滨. 周期为p ^m的广义割圆序列的 $ \frac{{p - 1}}{2}$ -错线性复杂度[J]. 电子与信息学报, 2013, 35(1): 191–195. doi: 10.3724/SP.J.1146.2012.00837 LIU Longfei, YANG Xiaoyuan, and CHEN Haibin. On the $ \dfrac{{p - 1}}{2}$-error linear complexity of generalized cyclotomic sequence with length p ^m[J]. Journal of Electronics &Information Technology, 2013, 35(1): 191–195. doi: 10.3724/SP.J.1146.2012.00837
[9]	吴晨煌, 许春香, 杜小妮. 周期为p²的q元序列的k-错线性复杂度[J]. 通信学报, 2019, 40(12): 21–28. doi: 10.11959/j.issn.1000-436x.2019230 WU Chenhuang, XU Chunxiang, and Du Xiaoni. k-error linear complexity of q-ary sequence of period p²[J]. Journal on Communications, 2019, 40(12): 21–28. doi: 10.11959/j.issn.1000-436x.2019230
[10]	陈智雄, 牛志华, 吴晨煌. 周期为素数平方的二元序列的k-错线性复杂度[J]. 密码学报, 2019, 6(5): 574–584. doi: 10.13868/j.cnki.jcr.000323 CHEN Zhixiong, NIU Zhihua, and WU Chenhuang. On k-error linear complexity of prime-square periodic binary sequences[J]. Journal of Cryptologic Research, 2019, 6(5): 574–584. doi: 10.13868/j.cnki.jcr.000323
[11]	MEIER W and STAFFELBACH O. The self-shrinking generator[C]. International Conference on the Theory and Applications of Cryptographic Techniques, Perugia, Italy, 1994: 205–214.
[12]	BLACKBURN S R. The linear complexity of the self-shrinking generator[J]. IEEE Transactions on Information Theory, 1999, 45(6): 2073–2077. doi: 10.1109/18.782139
[13]	KANSO A. Modified self-shrinking generator[J]. Computers and Electrical Engineering, 2010, 36(5): 993–1001. doi: 10.1016/j.compeleceng.2010.02.004
[14]	王锦玲, 邹慧仙. 关于m-序列模加实现的自缩序列[J]. 计算机工程与应用, 2015, 51(19): 110–113. doi: 10.3778/j.issn.1002-8331.1310-0089 WANG Jinling and ZOU Huixian. Self-shrinking sequence with modular addition on m-sequence[J]. Computer Engineering and Applications, 2015, 51(19): 110–113. doi: 10.3778/j.issn.1002-8331.1310-0089
[15]	王锦玲, 王娟, 陈忠宝. GF(3)上多位自收缩序列的模型与研究[M]. 何大可, 黄月江. 密码学进展——China Cypt’2007: 中国密码学会2007年会论文集. 成都: 西南交通大学出版社, 2007: 299–300. WANG Jinling, WANG Juan, and CHEN Zhongbao. The model and studying of multi-self-shrinking sequences on GF(3)[M]. HE D K, HUANG Y J. Progress on Cryptography——China Cypt’2007: Proceedings of 2007 Annual Meeting of Chinese Cryptology Society. Chengdu: Southwest Jiaotong University Press, 2007: 299–300.
[16]	王锦玲, 陈亚华, 兰娟丽. 扩展在上GF(3)新型自缩序列模型及研究[J]. 计算机工程与应用, 2009, 45(35): 114–119. doi: 10.3778/j.issn.1002-8331.2009.35.035 WANG Jinling, CHEN Yahua, and LAN Juanli. New model and studying of self-shrinking sequence developed on GF(3)[J]. Computer Engineering and Applications, 2009, 45(35): 114–119. doi: 10.3778/j.issn.1002-8331.2009.35.035
[17]	胡予璞, 张玉清, 肖国镇. 对称密码学[M]. 北京: 机械工业出版社, 2002: 66–74. HU Y P, ZHANG Y Q, XIAO G Z. Symmetric Key Cryptography[M]. Beijing: Machinery Industry Press, 2002: 66–74.
[18]	王慧娟, 王锦玲. GF(q)上广义自缩序列的线性复杂度[J]. 电子学报, 2011, 39(2): 414–418. WANG Huijuan and WANG Jinling. The linear complexity of the generalized self-shrinking generator on GF(q)[J]. Acta Electronica Sinica, 2011, 39(2): 414–418.
[19]	LIDL R and NIEDERREITER H. Finite Fields[M]. Reading, US: Addison-Wesley Publishing Company, 1983: 271–272.