周期为pq的平衡四元广义分圆序列的线性复杂度

doi:10.6040/j.issn.1671-9352.2.2015.230

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (9): 145-150.doi: 10.6040/j.issn.1671-9352.2.2015.230

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周期为pq的平衡四元广义分圆序列的线性复杂度

王国辉, 杜小妮^*, 万韫琦, 李芝霞

西北师范大学数学与统计学院, 甘肃兰州 730070

收稿日期:2015-09-21 出版日期:2016-09-20 发布日期:2016-09-23
通讯作者: 杜小妮(1972— ), 女,博士,教授,研究方向为密码学与信息安全. E-mail: ymLdxn@126.com E-mail:wanggh0039@126.com
作者简介:王国辉(1991— ),男,硕士研究生,研究方向为密码学与信息安全.E-mail:wanggh0039@126.com
基金资助:
国家自然科学基金资助项目(61202395,61462077);教育部“新世纪优秀人才计划”基金资助项目(NCET-12-0620);安徽省自然科学基金资助项目(1608085MF143)

Linear complexity of balanced quaternary generalized cyclotomic sequences with Period pq

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Received:2015-09-21 Online:2016-09-20 Published:2016-09-23

摘要/Abstract

摘要： 结合Gray映射和分圆理论,在Z4上构造了一类周期为pq的广义分圆序列。在有限域F_r(r≥5为奇素数)上确定新序列对应的傅里叶谱序列,并基于傅里叶谱序列的重量来确定新序列的线性复杂度。结果表明, 该序列具有良好的线性复杂度性质, 能够抗击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: 流密码, 傅里叶谱序列, 四元序列, 有限域, 线性复杂度

Abstract: Combined the theory of Gray mapping and cyclostomes, a new class of sequences over Z4 with Period pq was established. we will determine the corresponding Fourier spectral sequence of the new sequence on the finite field of F_r(r≥5, prime). Then, we will obtain the linear complexity of the new sequence from the weights of its Fourier spectral sequence. Results show that the sequences have larger linear complexity and can resist the attack by B-M algorithm. Its a good sequence from the viewpoint of cryptography.

Key words: stream ciphers, Fourier spectral sequence, linear complexity, quaternary sequence, finite field

中图分类号:

TN918

王国辉, 杜小妮, 万韫琦, 李芝霞. 周期为pq的平衡四元广义分圆序列的线性复杂度[J]. 山东大学学报（理学版）, 2016, 51(9): 145-150.

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周期为pq的平衡四元广义分圆序列的线性复杂度

Linear complexity of balanced quaternary generalized cyclotomic sequences with Period pq

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