一类长度为2p^(2)的二元序列的2-Adic复杂度研究  

2-Adic Complexity of a Class of Binary Sequences of Length 2p^(2)

作　　者：柯品惠[1,2] 卢栎羽 陈智雄[3] KE Pin-Hui;LU Li-Yu;CHEN Zhi-Xiong(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;Center for Applied Mathematics of Fujian Province(FJNU),Fuzhou 350117,China;Provincial Key Laboratory of Applied Mathematics,Putian University,Putian 351100,China)

机构地区：[1]福建师范大学数学与统计学院,福州350117 [2]福建省应用数学中心(福建师范大学),福州350117 [3]莆田学院应用数学福建省高校重点实验室,莆田351100

出　　处：《密码学报》2021年第4期560-571,共12页Journal of Cryptologic Research

基　　金：国家自然科学基金(61772292,61772476);福建省自然科学基金(2019J01273,2020J01905)。

摘　　要：伪随机序列的2-adic复杂度表示带进位反馈移位寄存器生成该序列的最短级数,它表明了该序列抵抗有理逼近攻击的能力.基于Xiong等人给出的研究方法,分析了一类长度为2p^(2)的广义割圆序列的2-adic复杂度.利用中国剩余定理和Zp上的"高斯周期"得到了Z_(2p^(2))上的"高斯周期".证明了上述序列的2-adic复杂度在许多情况下可以达到最大值.The 2-adic complexity of a sequence,which indicates the ability of the sequence to resist the rational approximation attack,is defined to be the shortest length of feedback-with-carry shift registers that can generate the sequence.By using a method introduced by Xiong et al.,the 2-adic complexity of a class of generalized cyclotomic sequences of length 2p^(2)is analyzed.Based on that,the"Gauss periods"over Z_(2p^(2))can be computed by using the Chinese Reminder Theorem and the well known"Gauss periods"over Zp.It is proved that in many cases,the 2-adic complexity of the aforementioned sequences reaches the maximum value.

关 键 词：伪随机序列 2-adic复杂度 高斯周期 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]