周期为p^m的q-元广义割圆序列的线性复杂度  

The Linear Complexity of q-ary Generalized Cyclotomic Sequences of Period p^m

作　　者：吴晨煌[1] 陈智雄[1] 杜小妮[2] 

机构地区：[1]莆田学院数学与应用数学系,福建莆田351100 [2]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《武汉大学学报（理学版）》2013年第2期129-136,共8页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61170246;61063041);福建省高校科技计划重点资助项目(JK2010047);福建省高校服务海西建设重点资助项目(2008HX03);福建省教育厅资助项目(JA12291;JB12179)

摘　　要：设p为素数且正整数q|(p-1).本文利用剩余类环Zpm构造q-阶广义割圆分类,定义周期为pm的q元广义割圆序列,推广了已有文献中关于二元广义割圆序列的构造,并确定了当q为奇素数与q=4时该类序列的线性复杂度.结果表明,该类序列的线性复杂度大于周期的一半,能抗击应用Berlekamp-Massey算法的安全攻击.同时,应用类似的构造方法,提出了周期为pm的p元广义割圆序列,并预测了该序列的线性复杂度的具体取值.Assume that p is a prime and q is a positive integer with ql（P--1）. Families of q-ary generalized cy- clotomic sequences of period pm are introduced by defining eneralized cyclotomic classes over Zp- and extended con- structions of certain binary generalized cyclotomic sequences in the literature. The linear complexities of such se- quences are determined when q is an odd prime or q： 4, respectively. The results indicate that the linear complexities are larger than a half of the period and such sequences can resist attacks by the Berlekamp-Massey algorithm. At the same time, a construction of p-ary generalized cyclotomic sequences of period pm is presented using the similar way and its linear complexity is conjectured.

关 键 词：流密码 伪随机序列 广义割圆序列 线性复杂度 剩余类环 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]