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  

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

作　　者：王艳[1] 薛改娜 李顺波[1] 惠飞飞 WANG Yan;XUE Gaina;LI Shunbo;HUI Feifei(School of Science,Xi’an University of Architecture and Technology,Xi’an 710055,China)

机构地区：[1]西安建筑科技大学理学院

出　　处：《电子与信息学报》2019年第9期2151-2155,共5页Journal of Electronics & Information Technology

基　　金：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)~~

摘　　要：该文基于Ding-广义分圆理论,将周期为2p^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。Based on the theory of Ding-generalized circle,a new class of generalized cyclotomic sequences of 2p^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.

关 键 词：广义分圆序列 线性复杂度 2次剩余类 BERLEKAMP-MASSEY算法 

分 类 号：TN918.4[电子电信—通信与信息系统]