周期为p^m的q-元广义割圆序列的线性复杂度

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 吴晨煌 WU Chenhuang1 1 first-author 陈智雄 CHEN Zhixiong1 1 杜小妮 DU Xiaoni2 2 莆田学院数学与应用数学系 莆田学院数学与应用数学系 Mathematics and Applied Mathematics Department,Putian University Mathematics and Applied Mathematics Department,Putian University 西北师范大学数学与信息科学学院 西北师范大学数学与信息科学学院 College of Mathematic and Information Science,Northwest Normal University College of Mathematic and Information Science,Northwest Normal University 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 q|（p-1）.Families of q-ary generalized cyclotomic sequences of period pm are introduced by defining eneralized cyclotomic classes over Zpm and extended constructions of certain binary generalized cyclotomic sequences in the literature.The linear complexities of such sequences 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. 流密码 伪随机序列 广义割圆序列 线性复杂度 剩余类环 stream cipher pseudorandom sequences generalized cyclotomic sequences linear complexity residue class rings 10.14188/j.1671-8836.2013.02.004 TN918.1 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） 2013-02-01 2021-04-01 2 59