王艳,
薛改娜^,,
李顺波,
惠飞飞
西安建筑科技大学理学院 西安 710055
基金项目:国家自然科学基金(11471255)，西安建筑科技大学自然科学专项(1609718034)，西安建筑科技大学人才基金(RC1338)

详细信息

作者简介:王艳：女，1982年生，副教授，研究方向为序列密码
薛改娜：女，1992年生，硕士生，研究方向为序列密码
李顺波：男，1979年生，副教授，研究方向为流密码分析
惠飞飞：女，1992年生，硕士生，研究方向为流密码分析

通讯作者:薛改娜　392455200@qq.com

中图分类号:TN918.4

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出版历程

收稿日期:2018-09-18
修回日期:2019-06-06
网络出版日期:2019-06-28
刊出日期:2019-09-10

The Linear Complexity of a New Class of Generalized Cyclotomic Sequence of Order q with Period 2p^m

Yan WANG,
Gaina XUE^,,
Shunbo LI,
Feifei HUI
School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China
Funds:The National Natural Science Foundation of China (11471255), The Natural Science Project of Xi’an University of Architecture and Technology (1609718034), The Talent Fund of Xi’an University of Architecture and Technology (RC1338)


摘要
摘要:该文基于Ding-广义分圆理论，将周期为$ 2{p^m}$($ p$为奇素数，$ m$为正整数)广义分圆序列的研究推广到任意素数阶情形，构造了一类新序列。通过数论方法分析多项式广义分圆类，确定并计算线性复杂度与序列的2次剩余类和2次非剩余类的划分紧密相关。结果表明该类序列的线性复杂度远远大于周期的一半，能抗击应用Berlekamp-Massey(B-M)算法的安全攻击，是密码学意义上性质良好的伪随机序列。
关键词:广义分圆序列/
线性复杂度/
2次剩余类/
Berlekamp-Massey算法
Abstract:Based on the theory of Ding - generalized circle, a new class of generalized cyclotomic sequences of $ 2{p^m}$ ($ p$ odd prime and m>1) with arbitrary prime order is constructed in this paper. The polynomial cyclotomic classes are analysed by algebra number theory method. Moreover, the linear complexity of the new sequences are determined, which losely related to the division of quadratic residual classes and quadratic non-residual classes. Results show that the linear complexity of this kind of sequence is much larger than half of the period, hence, can fight Berlekamp-Massey’s security application attack that is a pseudo-random sequence with good properties in the sense of cryptography.
Key words:Generalized cyclotomic sequence/
Linear complexity/
Secondary residual class/
Berlekamp-Massey (B-M) algorithm



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