一类新的pqr长2阶广义分圆序列的线性复杂度

doi:10.3969/j.issn.0372-2112.2015.01.026

电子学报 ›› 2015, Vol. 43 ›› Issue (1): 166-170.DOI: 10.3969/j.issn.0372-2112.2015.01.026

一类新的pqr长2阶广义分圆序列的线性复杂度

常祖领¹, 周玉倩², 柯品惠³

1. 郑州大学数学与统计学院, 河南郑州 450001;
2. 北京邮电大学网络与交换技术研究院, 北京 100876;
3. 福建师范大学网络安全与密码技术重点实验室, 福建福州 350007

收稿日期:2013-09-27 修回日期:2013-12-09 出版日期:2015-01-25
- 作者简介:
- 常祖领 男, 1976年12月出生, 河南新乡人.副教授、硕士生导师, 1998年和2003年分别在南开大学获理学学士和理学博士学位, 现在郑州大学数学与统计学院工作, 主要从事信息论、密码序列设计等方面的研究工作.E-mail:zuling_chang@zzu.edu.cn;周玉倩 女, 1989年1月出生, 河南新乡人.现为北京邮电大学网络与交换技术研究院博士生, 主要从事量子密码、密码序列设计等方面的研究工作;柯品惠 男, 1978年9月出生, 福建建阳人.福建师范大学数学与计算机科学学院副教授, 主要从事序列设计、编码密码学等方面的研究工作.
- 基金资助:
- 国家自然科学基金联合基金 (No.U1304604); 国家自然科学基金青年基金 (No.61102093); 河南省教育厅科学技术研究重点项目 (No.14A110022)

Linear Complexity of New Generalized Cyclotomic Sequences of Order Two and Length pqr

CHANG Zu-ling¹, ZHOU Yu-qian², KE Pin-hui³

1. Department of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China;
2. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China;
3. Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fuzhou, Fujian 350007, China

Received:2013-09-27 Revised:2013-12-09 Online:2015-01-25 Published:2015-01-25
- Supported by:
- Joint Funds of the National Natural Science Foundation of China (No.U1304604); Youth Fund of National Natural Science Foundation of China (No.61102093); Key Project of Science and Technology Research of Education Department of Henan Province (No.14A110022)

摘要/Abstract

摘要：

具有良好随机性质的伪随机序列在流密码和通信领域中有着广泛的应用.本文构造出一类新的长为pqr的2阶广义分圆序列,并且计算其线性复杂度和极小多项式.结果显示这种序列具有高线性复杂度.

关键词: 广义分圆序列, 线性复杂度, 极小多项式

Abstract:

Pseudorandom sequences with good randomness properties are widely used in stream ciphers and communications.This paper introduces one new class of generalized cyclotomic sequences of order two and length pqr, then calculates the linear complexity and the minimal polynomial of these sequences.The results show that the new cyclotomic sequences have high linear complexity.

Key words: generalized cyclotomic sequences, linear complexity, minimal polynomial

中图分类号:

TN918.1

常祖领, 周玉倩, 柯品惠. 一类新的pqr长2阶广义分圆序列的线性复杂度[J]. 电子学报, 2015, 43(1): 166-170.

CHANG Zu-ling, ZHOU Yu-qian, KE Pin-hui . Linear Complexity of New Generalized Cyclotomic Sequences of Order Two and Length pqr[J]. Acta Electronica Sinica, 2015, 43(1): 166-170.

参考文献

[1] J L Massey.Shift register synthesis and BCH decoding [J].IEEE Trans on Information Theory,1969,15(1):122-127.
[2] C Ding.Autocorrelation values of generalized cyclotomic sequences of order two [J].IEEE Trans on Information Theory,1998,44(4):1698-1702.
[3] C Ding.Linear complexity of generalized cyclotomic binary sequences of order 2 [J].Finite Fields and Their Applications,1997,3(2):159-174.
[4] E Bai,X Fu,G Xiao.On the linear complexity of generalized cyclotomic sequences of order four over Z_pq[J].IEICE Trans on Fundamentals,2005,E88-A(1):392-395.
[5] E Bai,X Liu.Generalized cyclotomic sequences of order four over Z_pq and their autocorrelation values [J].Chinese Journal of Engineering Mathematics,2008,25(5):894-900.
[6] S Li,L Zhou.Linear complexity of a new generalized cyclotomic sequences of order four and length pq [A].International Conference on Communications,Circuits and Systems(ICCCAS)[C].USA:IEEE,2009.331-334.
[7] T Yan,S Li,G Xiao.On the linear complexity of generalized cyclotomic sequences with the period p^m[J].Applied Mathematics Letters,2008,21(2):187-193.
[8] V A Edemskiy.About computation of the linear complexity of generalized cyclotomic sequences with period pⁿ⁺¹[J].Designs,Codes and Cryptography,2011,61(3):251-260.
[9] J Zhang,C A Zhao,X Ma.Linear complexity of generalized cyclotomic binary sequences with period 2p^m[A].The 17th International Symposium on Applied Algebra,Algebraic Algorithms and Error-Correcting Codes(AAECC-17)[C].Bangalore,India,2007.93-108.
[10] P Ke,J Zhang,S Zhang.On the linear complexity and the autocorrelation of generalized cyclotomic binary sequences with period 2p^m[J].Designs,Codes and Cryptography,2012,67(3):325-339.
[11] L Hu,Q Yue,M Wang.The linear complexity of Whiteman's generalized cyclotomic sequences of period p^m+1qⁿ⁺¹[J].IEEE Trans on Information Theory,2012,58(8):5534-5543.
[12] C Ding,T Helleseth.Generalized cyclotomic codes of length p^e₁₁…pe_t_t[J].IEEE Trans on Information Theory,1999,45(2):467-474.
[13] 张禾瑞.近世代数基础(修订版)[M].北京:高等教育出版社,2010.
[14] R Lidl,H Neiderreiter.Finite Fields [M].MA:Addison-Wesley,1983.
[15] 冯登国,等.密码学原理与实践(第3版)[M].北京:电子工业出版社,2009.147-148.

一类新的pqr长2阶广义分圆序列的线性复杂度

Linear Complexity of New Generalized Cyclotomic Sequences of Order Two and Length pqr

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

[1]	赵璐, 刘春红, 杜蛟, 曹天庆. Z₄上两类具有最优自相关四元序列的线性复杂度研究[J]. 电子学报, 2021, 49(4): 631-636.
[2]	柯品惠, 李瑞芳, 张胜元. 一类新的周期为p^m+1qⁿ⁺¹的二元广义分圆序列的线性复杂度[J]. 电子学报, 2014, 42(5): 1009-1013.
[3]	杜小妮;陈智雄. 关于Legendre序列迹表示的注记[J]. 电子学报, 2011, 39(4): 869-871.
[4]	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.
[5]	皮飞;戚文峰;. 二元周期序列的4-错线性复杂度[J]. 电子学报, 2011, 39(12): 2914-2920.
[6]	刁哲军;陈嘉兴;刘志华. 一种具有大线性复杂度伪随机序列的构造[J]. 电子学报, 2008, 36(10): 1961-1965.
[7]	高军涛, 胡予濮, 李雪莲. 自相关性和线性复杂度的关系[J]. 电子学报, 2006, 34(8): 1401-1404.
[8]	陈嘉兴, 周廷显, 许成谦. 一种快速构造具有最大线性复杂度GMW序列的方法[J]. 电子学报, 2005, 33(5): 857-859.
[9]	苏明;符方伟. 随机周期序列k错线性复杂度的方差估计[J]. 电子学报, 2005, 33(2): 279-283.
[10]	赵耀东, 戚文峰. 二元周期序列的k错误线性复杂度[J]. 电子学报, 2005, 33(1): 12-16.
[11]	魏仕民. 确定周期序列k错线性复杂度的一个快速算法[J]. 电子学报, 2004, 32(5): 705-708.
[12]	魏仕民;陈钟;段云所. 周期序列球体复杂度的一个新算法[J]. 电子学报, 2003, 31(8): 1263-1265.
[13]	胡予濮. 一类稀疏序列的最小周期[J]. 电子学报, 2003, 31(4): 616-619.
[14]	胡予濮. 一类理想自相关序列的伪随机性[J]. 电子学报, 2003, 31(2): 245-247.
[15]	胡予濮;杨波. 伪随机稀疏序列的研究[J]. 电子学报, 2002, 30(1): 142-144.