杜小妮,
李丽^,,
张福军
西北师范大学数学与统计学院 兰州 730070
基金项目:国家自然科学基金(61462077, 61562077, 61772022)，上海市自然科学基金(16ZR1411200)

详细信息

作者简介:杜小妮：女，1972年生，教授，博士生导师，研究方向为密码学与信息安全
李丽：女，1991年生，硕士生，研究方向为密码学与信息安全
张福军：男，1995年生，硕士生，研究方向为密码学与信息安全

通讯作者:李丽　ymxlili36@126.com

中图分类号:TN918.4

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出版历程

收稿日期:2019-01-24
修回日期:2019-06-20
网络出版日期:2019-07-09
刊出日期:2019-12-01

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

Xiaoni DU,
Li LI^,,
Fujun ZHANG
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Funds:The National Natural Science Foundation of China (61462077, 61562077, 61772022), The Shanghai Municipal Natural Science Foundation (16ZR1411200)


摘要
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$2{p^m}$($p$为奇素数，整数$m \ge 1$)的欧拉商构造了一类周期为$2{p^{m + 1}}$的二元序列，并在${2^{p - 1}}\not \equiv 1 ({od}\,{p^2})$的条件下借助有限域${F_2}$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。
关键词:有限域/
二元序列/
欧拉商/
线性复杂度/
极小多项式
Abstract: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 $2{p^{m + 1}}$ is constructed using Euler quotients modulo $2{p^m},$ where $p$ is an odd prime and integer $m \ge 1.$ Under the condition of ${2^{p - 1}}\not \equiv 1 ({od}\,{p^2})$, the linear complexity of the sequence is examined with the method of determining the roots of polynomial over finite field ${F_2}$. 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.
Key words:Finite fields/
Binary sequences/
Euler quotients/
Linear complexity/
Minimal polynomial



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