本原σ-LFSR序列距离向量的计算

doi:1000-436X（2011）09-0033-05

通信学报 ›› 2011, Vol. 32 ›› Issue (9): 33-37.doi: 1000-436X（2011）09-0033-05

本原σ-LFSR序列距离向量的计算

谭刚敏¹,曾光¹,韩文报¹,张娜²

¹ 信息工程大学信息工程学院，河南郑州 450002
² 解放军95833部队，北京 100092

出版日期:2012-09-25 发布日期:2017-05-28
基金资助:
：国家自然科学基金资助项目;国家重点基础研究发展计划（“973”计划）基金资助项目;教育部新世纪优秀人才支持计划资助;全国优秀博士学位论文作者专项基金资助项目

Calculation of interval vectors of primitive σ-LFSR sequences

Gang-min TAN¹,Guang ZENG¹,Wen-bao HAN¹,Na ZHANG²

¹ Institute of Information Engineering,Information Engineering University,Zhengzhou 450002,China
² Unit 95833 of the PLA,Beijing 100092,China

Online:2012-09-25 Published:2017-05-28
Supported by:
The National Natural Science Foundation of China;The National High Technology Research and Development Program of China（863 Program）;The National Basic Research Program of China（973 Program）;The New Century Excellent Talents in University Education Ministry of China;Foundation for the Author of National Excellent Doctoral Dissertation of China

摘要/Abstract

摘要：

证明了本原σ-线性反馈移位寄存器（σ-LFSR）序列距离向量的计算与有限域上离散对数的计算等价，同时给出一个本原σ-LFSR序列距离向量的计算方法。还给出一类特殊本原σ-LFSR序列距离向量的计算方法，该方法将有限域上离散对数的计算转化到其子域上离散对数的计算，复杂度显著降低。

关键词: 序列密码, 本原σ-LFSR, 距离向量, 离散对数

Abstract:

The equivalence between calculation of interval vectors of primitive σ-linear feedback shift register（σ-LFSR）sequences and calculation of discrete logarithms over finite field was proved,at the same time a calculation method for interval vectors of primitive σ-LFSR sequences was given.Then another calculation method for interval vectors of a class of primitive σ-LFSR sequences was obtained,which converted the calculation of discrete logarithms over finite field to its subfield and the complexity was much lower.

Key words: stream cipher, primitive σ-LFSR, interval vector, discrete logarithm

谭刚敏,曾光,韩文报,张娜. 本原σ-LFSR序列距离向量的计算[J]. 通信学报, 2011, 32(9): 33-37.

Gang-min TAN,Guang ZENG,Wen-bao HAN,Na ZHANG. Calculation of interval vectors of primitive σ-LFSR sequences[J]. Journal on Communications, 2011, 32(9): 33-37.

图/表 1

参考文献 12

[1]	The eSTREAM project[EB/OL]. , 2009.
[2]	BERBAIN C , BILLET O , CANTEAUT A , et al. SOSEMANUK,a fast software-oriented stream cipher[A]. New Stream Designs[C]. Berlin, 2008.98-118.
[3]	ISO/IEC 18033-4:2005.Information Technology-Security Techniques-Encryption Algorithms-Part4:Stream Ciphers[S]. Geneva:ISO/IEC, 2005.
[4]	EKDAHL P , JOHANSSON T . A new version of the stream cipher SNOW[A]. 9th Annual International Workshop on Selected Areas in Cryptography（SAC2002）[C]. Berlin, 2002.47-61.
[5]	ZENG G , HE K C , HAN W B . A trinomial type of σ-LFSR oriented toward software implementation[J]. Science in China Series F:Information Sciences, 2007,50(3): 359-372.
[6]	CHORPADE S R , HASAN S U , KUMARI M . Primitive polynomials,singer cycles,and σ-LFSRs[EB/OL]. . 2009.
[7]	ZENG G , HAN W B , HE K C . High efficiency feedback shift register:σ-LFSR[EB/OL]. Cryptology ePrint Archive,Report 2007/114 , 2007.
[8]	张猛，曾光，韩文报等. 本原σ-LFSR序列的迹表示及其应用[J]. 电子与信息学报， 2009,31(4):942-945. ZHANG M , ZENG G , HAN W B , et al. Trace representation of primitive σ-LFSR sequences and its application[J]. Journal of Electronics ＆Information Technology, 2009,31(4):942-945.
[9]	HAWKES P , ROSE G . Primitive specification and supporting documentation for sober-t32 submission to NESSIE[A]. Proceedings of the first NESSIE Workshop[C]. Heverlee,Belgium, 2000.
[10]	STINSON D R . Cryptography:Theory and Practice（Third Edition）[M]. Boca Raton,FL： Chapman ＆ Hall/CRC Press LLC, 2006.
[11]	PARK W J , KOMO J J . Relationships between m-sequences over GF（q）and GF（qm）[J]. IEEE Transaction on Information Theory, 1989,35(1): 183-186.
[12]	LIDI R , NIEDERREITER H . Finite Fields[M]. New Jersey： Addison-Wesley Publishing Company, 1983.

i	e_i	i	e_i
1	3861931267	16	3761994729
2	2421774986	17	3328958701
3	1988738958	18	1142407923
4	1555702930	19	709371895
5	75218143	20	276335867
6	1869543289	21	3720160510
7	1436507261	22	2119808904
8	2084415919	23	1686772876
9	1651379891	24	3495508446
10	2249100343	25	3062472418
11	1816064315	26	1997445520
12	1383028287	27	1564409492
13	613435183	28	1131373464
14	2966708643	29	3720883070
15	2533672615	30	866072056
		31	433036028

[1]	王艳,李顺波,薛改娜. SLCE序列的2-adic复杂度[J]. 通信学报, 2019, 40(8): 151-156.
[2]	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.
[3]	秦艳琳,吴晓平,胡卫. 高效的无证书多接收者匿名签密方案[J]. 通信学报, 2016, 37(6): 129-136.
[4]	樊爱宛,杨照峰,谢丽明. 强安全无证书签名方案的安全性分析和改进[J]. 通信学报, 2014, 35(5): 118-123.
[5]	樊爱宛1，杨照峰1，谢丽明2. 强安全无证书签名方案的安全性分析和改进法[J]. 通信学报, 2014, 35(5): 16-123.
[6]	游伟,戚文峰. 单圈T-函数的2-adic复杂度和1-错2-adic复杂度[J]. 通信学报, 2014, 35(3): 135-139.
[7]	张德栋,马兆丰,杨义先,钮心忻. 群签名中成员撤销问题解决方案[J]. 通信学报, 2014, 35(3): 193-200.
[8]	游伟1，戚文峰2,3. 单圈T-函数的2-adic复杂度和1-错2-adic复杂度[J]. 通信学报, 2014, 35(3): 15-139.
[9]	张德栋1，马兆丰2，杨义先2，钮心忻2. 群签名中成员撤销问题解决方案[J]. 通信学报, 2014, 35(3): 22-200.
[10]	王亚飞,张睿哲. 强安全无对的无证书签名方案[J]. 通信学报, 2013, 34(2): 94-99.
[11]	高海英,金晨辉. 基于多个独立区分特征的序列密码最优联合区分器[J]. 通信学报, 2012, 33(7): 44-48.
[12]	王圣宝,刘文浩,谢琪. 无双线性配对的无证书签名方案[J]. 通信学报, 2012, 33(4): 93-98.
[13]	田有亮,马建峰,彭长根,陈曦. 椭圆曲线上的信息论安全的可验证秘密共享方案[J]. 通信学报, 2011, 32(12): 96-102.
[14]	杨阳,曾光. 序列密码算法RAKAPOSHI的动态移存器构造[J]. 通信学报, 2011, 32(11A): 178-183.
[15]	李鹤龄,戚文峰. F_p上pⁿ-周期序列的k-错误序列[J]. 通信学报, 2010, 31(6): 19-24.

本原σ-LFSR序列距离向量的计算

Calculation of interval vectors of primitive σ-LFSR sequences

在线阅读

PDF下载

可视化

摘要/Abstract

引用本文

使用本文

图/表 1

参考文献 12

相关文章 15

Metrics

推荐阅读 0