F_(q)上一类周期为2p^(2)的四元广义分圆序列的线性复杂度  

Linear Complexity over F_(q) of a Class of Generalized Cyclotomic Quaternary Sequences with Period 2p^(2)

作　　者：王艳[1] 相乃姣 韩西林 闫联陶 WANG Yan;XIANG Naijiao;HAN Xilin;YAN Liantao(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,西安710055

出　　处：《电子与信息学报》2021年第10期2936-2943,共8页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(61902304);陕西省自然科学基础研究计划资助项目(2021JQ-495)。

摘　　要：该文基于广义分圆理论,通过计算F_(q)(q=r^(m))上的序列生成多项式的零点个数,确定了一类周期为2p^(2)的四元广义分圆序列的极小多项式和线性复杂度。结果表明,该序列的线性复杂度大于其周期的1/2,能够有效地抵抗Berlekamp-Massey(B-M)算法的攻击,是密码学意义上一类良好的周期伪随机序列。Based on the theory of generalized cyclotomy,the minimal polynomial and linear complexity of a class of generalized cyclotomic quaternary sequences with period 2p^(2)are determined by explicitly computing the number of zeros of the generating polynomial over F_(q)(q=r^(m))The results show that the linear complexity is more than p^(2),the half of the period 2p^(2)According to Berlekamp-Massey algorithm,these sequences can be viewed as enough good for the utilizing in cryptography.

关 键 词：广义分圆序列 4元序列 线性复杂度 生成多项式 极小多项式 

分 类 号：TN918.4[电子电信—通信与信息系统]