一类新的周期为p3的GF(l)上广义割圆序列的线性复杂度

doi:10.6040/j.issn.1671-9352.2.2016.108

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (3): 24-31.doi: 10.6040/j.issn.1671-9352.2.2016.108

一类新的周期为p³的GF(l)上广义割圆序列的线性复杂度

刘龙飞,杨晓元

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

收稿日期:2016-08-18 出版日期:2017-03-20 发布日期:2017-03-20
作者简介:刘龙飞(1990— ),男,硕士,讲师,研究方向为流密码和编码. E-mail: ya_zhou_521@163.com
基金资助:
国家自然科学基金资助项目(61562077,61462077);国家社会科学基金资助项目(16BTJ033);武警工程大学基础研究基金(WJY201518);武警工程大学军事理论研究项目(JLX201648)

On the linear complexity of a new generalized cyclotomic sequence with length p³ over GF(l)

LIU Long-fei, YANG Xiao-yuan

Key Laboratory of Network &
Information Security of Armed Police Force, Engineering University of Armed Police Force, Xian 710086, Shaanxi, China

Received:2016-08-18 Online:2017-03-20 Published:2017-03-20

摘要/Abstract

摘要： 线性复杂度是度量序列随机性的一个重要指标。基于Ding-广义割圆序列,构造了GF(l)上一类新的周期为p3的广义割圆序列(其中l为一奇素数h的幂),且该序列为平衡序列,并通过有限域上的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,以它们做密钥流序列的密码系统具有抵抗B-M算法攻击的能力。

关键词: 密码学, 流密码, 伪随机序列, 线性复杂度, 广义割圆类

Abstract: Linear complexity is the most important index for measuring the randomness properties of sequences. Based on the Ding-generalized cyclotomy, a new class of generalized cyclotomic sequences with length p³ over the finite field of power of odd prime order is constructed, and the sequence is balanced. The linear complexity of the sequences is determined using 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: pseudo-random sequence, generalized cyclotomy, cryptography, linear complexity, stream cipher

中图分类号:

TP309

刘龙飞,杨晓元. 一类新的周期为p³的GF(l)上广义割圆序列的线性复杂度[J]. 山东大学学报（理学版）, 2017, 52(3): 24-31.

LIU Long-fei, YANG Xiao-yuan. On the linear complexity of a new generalized cyclotomic sequence with length p³ over GF(l)[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(3): 24-31.

参考文献

[1] DING Cunsheng. Linear complexity of generalized cyclotomic binary sequences of order 2[J]. Finite Fields and Their Applications, 1997, 8:159-174.
[2] DING Cunsheng, HELLESETH T. New generalized cyclotomy and its applications[J]. Finite Fields and Their Applications, 1998, 4(2):140-166.
[3] CUSICK T W, DING Cunsheng, RENVALL A. Stream Ciphers and Number Theory[M]. Elsevier Science Pub Co, 1998, Chapter 3-8.
[4] YAN Tongjiang, HUANG Bingjia, XIAO Guozhen. Cryptographic properties of some binary generalized cyclotomic sequences with the length p²[J]. Information Sciences, 2008, 178(3):1078-1086.
[5] KIM Y, JIN S, SONG H. Linear complexity and autocorrelation of prime cube sequences[J]. Applicable Algebra in Engineering, Communication and Computing, 2007, LNCS 4851, 188-197.
[6] YAN Tongjiang, LI Shengqiang, XIAO Guozhen. On the linear complexity of generalized cyclotomic sequences with the period p^m[J]. Applied Mathematics Letters, 2008, 21(2):187-193.
[7] DU Xiaoni, CHEN Zhixiong. Trace representation of binary generalized cyclotomic sequences with length p^m[J]. IEICE Transaction on Fundamentals, 2011, E94-A(2):761-765.
[8] EDEMSKIY Vladimir. About computation of the linear complexity of generalized cyclotomic sequences with period pⁿ⁺1[J]. International Journal of Soft Computing and Engineering, 2011, 1(3):2231-2307.
[9] WANG Qiuyan, JIANG Yupeng, LIN Dongdai. Linear complexity of binary generalized cyclotomic sequences over GF(q)[J]. Journal of Complexity, 2015, 31(5), 731-740.
[10] WANG Qiuyan, JIANG Yupeng, LIN Dongdai. Linear complexity of Ding-Helleseth sequences of order 2 over GF(l)[J]. Cryptography and Communications, 2015, DOI 10,1007/s12095-015-0138-5.
[11] FAN Cuiling, GE Gennian. A unified approach to whitemans and ding-helleseths generalized cyclotomy over residue class rings[J]. IEEE Transactions on Information Theory, 2014, 60(2):1326-1336.
[12] DING Cunsheng. Cyclic codes from the two primes sequences[J]. IEEE Transactions on Information Theory, 2012, 58(6):3881-3891.
[13] DING Cunsheng. Cyclic codes from cyclotomic sequences of order four[J]. Finite Fields and Their Applications, 2013, 23(1):8-34.
[14] ZENG Xiangyong, CAI Han, TANG Xiaohu, et al. Optimal frequency Hopping sequences of odd length[J]. IEEE Transactions on Information Theory, 2013, 59(5):3237-3248.
[15] CAI Han, ZHOU Zhengchun, YANG Yang, et al. A New construction of frequency-hopping sequences optimal partial hamming correlation[J]. IEEE Transactions on Information Theory, 2014, 60(9):5782-5790.
[16] CAI Han, LIANG Hongbin, TANG Xiaohu. Constructions of optimal 2-D optical orthogonal codes via generalized cyclotomic classes[J]. IEEE Transactions on Information Theory, 2015, 61(1):688-695.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

一类新的周期为p³的GF(l)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 p³ over GF(l)

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 7

多维度评价

本文评价

推荐阅读 0

[1]	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.
[2]	张方国. 椭圆曲线在密码中的应用:过去,现在,将来…[J]. J4, 2013, 48(05): 1-13.
[3]	巨春飞1,仇晓涛2,王保仓2,3. 基于矩阵环的快速公钥密码算法[J]. J4, 2012, 47(9): 56-59.
[4]	关杰, 张应杰. “与常数模2ⁿ加”运算的不可能差分性质研究[J]. J4, 2010, 45(11): 47-51.
[5]	王锦玲兰娟丽. GF(q)上一类新型的广义自缩序列[J]. J4, 2009, 44(10): 91-96.
[6]	王锦玲,刘宗成 . 主控生成器[J]. J4, 2008, 43(1): 81-87 .
[7]	于静之,张文英,刘祥忠 . 根据连续2^n-1个状态写出单圈T函数ANF的方法[J]. J4, 2007, 42(4): 14-18 .