基于模2p^m的欧拉商的二元序列的线性复杂度  

Linear Complexity of Binary Sequences Derived from Euler Quotients Modulo 2p^m

作　　者：杜小妮 李丽 张福军 DU Xiaoni;LI Li;ZHANG Fujun(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院

出　　处：《电子与信息学报》2019年第12期3000-3005,共6页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(61462077,61562077,61772022);上海市自然科学基金(16ZR1411200)~~

摘　　要：基于欧拉商模奇素数幂构造的伪随机序列均具有良好的密码学性质。该文根据剩余类环理论,利用模2pm(p为奇素数,整数m≥1)的欧拉商构造了一类周期为2p^m+1的二元序列,并在2^p-1■1(mod p^2)的条件下借助有限域F2上确定多项式根的方法,给出了序列的线性复杂度。结果表明,序列的线性复杂度取值为2(p^m+1-p)或2(p^m+1-1)不小于其周期的1/2,能够抵抗Berlekamp-Massey(B-M)算法的攻击,是密码学意义上性质良好的伪随机序列。Families of pseudorandom sequences derived from Euler quotients modulo odd prime power possess sound cryptographic properties.In this paper,according to the theory of residue class ring,a new classes of binary sequences with period 2p^m+1 is constructed using Euler quotients modulo 2 p^m;where p is an odd prime and integer m≥1:Under the condition of 2^p-1■1(mod p^2),the linear complexity of the sequence is examined with the method of determining the roots of polynomial over finite field F2.The results show that the linear complexity of the sequence takes the value 2(p^m+1-p)or 2(p^m+1-1),which is larger than half of its period and can resist the attack of Berlekamp-Massey(B-M)algorithm.It is a good sequence from the viewpoint of cryptography.

关 键 词：有限域 二元序列 欧拉商 线性复杂度 极小多项式 

分 类 号：TN918.4[电子电信—通信与信息系统]