新的周期为pm的GF(h)上广义割圆序列的线性复杂度

doi:10.11959/j.issn.1000-436x.2017181

通信学报 ›› 2017, Vol. 38 ›› Issue (9): 39-45.doi: 10.11959/j.issn.1000-436x.2017181

新的周期为p^m的GF(h)上广义割圆序列的线性复杂度

刘龙飞¹,杨凯¹,杨晓元^1,²

¹ 武警工程大学网络与信息安全武警部队重点实验室，陕西西安 710086
² 西安电子科技大学计算机网络与信息安全教育部重点实验室，陕西西安 710071

修回日期:2017-04-05 出版日期:2017-09-01 发布日期:2017-10-18
作者简介:刘龙飞（1990-），男，河南沈丘人，武警工程大学讲师，主要研究方向为流密码和编码。|杨凯（1983-），男，山东莱芜人，武警工程大学讲师，主要研究方向为信息安全。|杨晓元（1959-），男，湖南湘潭人，武警工程大学教授、博士生导师，主要研究方向为密码学和信息安全。
基金资助:
国家密码发展基金资助项目(MMJJ20170112);国家重点研发计划基金资助项目(2017YFB0802002);国家自然科学基金资助项目(61562077);国家自然科学基金资助项目(U1636114);国家自然科学基金资助项目(64572521);国家自然科学基金资助项目(61402530);武警工程大学基础研究基金资助项目(WJY201518)

On the linear complexity of a new generalized cyclotomic sequence with length ^mover GF(h)

Long-fei LIU¹,Kai YANG¹,Xiao-yuan YANG^1,²

¹ Key Laboratory of Network ＆Information Security of Armed Police Force,Engineering University of Armed Police Force,Xi’an 710086,China
² Key Laboratory of Computer Network ＆Information Security of the Ministry of Education,Xidian University,Xi’an 710071,China

Revised:2017-04-05 Online:2017-09-01 Published:2017-10-18
Supported by:
The National Cryptography Development Fund of China(MMJJ20170112);The National Key Research and Development Program of China(2017YFB0802002);The National Natural Science Foundation of China(61562077);The National Natural Science Foundation of China(U1636114);The National Natural Science Foundation of China(64572521);The National Natural Science Foundation of China(61402530);The Basic Research Foundation of Engineering College of APF(WJY201518)

摘要/Abstract

摘要：

基于Ding-广义割圆序列，构造了GF(h)上一类新的周期为p^m的广义割圆序列，且该序列为平衡序列。通过分析h与p的关系及多项式理论，确定了该序列的线性复杂度。结果表明，该类序列具有良好的线性复杂度性质，将它们作为密钥流序列的密码系统具有抵抗Berlekamp-Massey算法攻击的能力。

关键词: 流密码, 伪随机序列, 广义割圆类, 线性复杂度

Abstract:

Based on the Ding-generalized cyclotomy,a new class of generalized cyclotomic sequences with length p^m over the finite field of power of odd prime order was constructed,and the sequence was balanced.The linear complexity of the sequences was determined using the relationship between h and p and the theory of polynomial over finite field.It is shown that the sequence has good linear complexity,and it can resist attacks from the application of the Berlekamp-Massey algorithm.

Key words: stream cipher, pseudo-random sequence, generalized cyclotomy, linear complexity

中图分类号:

TP302

刘龙飞,杨凯,杨晓元. 新的周期为p^m的GF(h)上广义割圆序列的线性复杂度[J]. 通信学报, 2017, 38(9): 39-45.

Long-fei LIU,Kai YANG,Xiao-yuan YANG. On the linear complexity of a new generalized cyclotomic sequence with length ^mover GF(h)[J]. Journal on Communications, 2017, 38(9): 39-45.

图/表 1

表1

参考文献 21

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序列	域	周期	最大线性复杂度	最小线性复杂度
文献[20]构造序列	GF(2)	p	p	$\frac{p - 1}{2}$
文献[21]构造序列	GF(q)	n	n	$\frac{n - 1}{2}$
文献[4]构造序列	GF(2)	p²	p²	$\frac{p^{2} + 1}{2}$
文献[18]构造序列	GF(q)	n²	n²	$\frac{n^{2} - 1}{2}$
文献[6]构造序列	GF(2)	p^m	p^m	$\frac{p^{m} + 1}{2}$
本文构造序列	GF(h)	p^m	p^m	$p^{m} - (\frac{p^{m - 1} (p - 1)}{2} + \dots + \frac{p (p - 1)}{2} + \frac{p - 1}{2}) - 1$

新的周期为p^m的GF(h)上广义割圆序列的线性复杂度

On the linear complexity of a new generalized cyclotomic sequence with length ^mover GF(h)

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新的周期为pm的GF(h)上广义割圆序列的线性复杂度

On the linear complexity of a new generalized cyclotomic sequence with length mover GF(h)

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新的周期为p^m的GF(h)上广义割圆序列的线性复杂度

On the linear complexity of a new generalized cyclotomic sequence with length ^mover GF(h)