Linear Complexity of Quaternary Sequences over Z4 Derived from Generalized Cyclotomic Classes Modulo 2p2

Xiaoni DU; Liping ZHAO; Lianhua WANG

doi:10.11999/JEIT180189

Volume 40 Issue 12

Nov. 2018

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Xiaoni DU, Liping ZHAO, Lianhua WANG. Linear Complexity of Quaternary Sequences over Z4 Derived from Generalized Cyclotomic Classes Modulo 2p2[J]. Journal of Electronics & Information Technology, 2018, 40(12): 2992-2997. doi: 10.11999/JEIT180189

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Xiaoni DU, Liping ZHAO, Lianhua WANG. Linear Complexity of Quaternary Sequences over Z₄ Derived from Generalized Cyclotomic Classes Modulo 2p²[J]. Journal of Electronics & Information Technology, 2018, 40(12): 2992-2997. doi: 10.11999/JEIT180189

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Linear Complexity of Quaternary Sequences over Z₄ Derived from Generalized Cyclotomic Classes Modulo 2p²

doi: 10.11999/JEIT180189

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

Funds: The National Natural Science Foundation of China (61462077, 61772022), Anhui Province Natural Science Foundation (1608085MF143), Shanghai Municipal Natural Science Foundation (16ZR1411200)

Received Date: 2018-02-11
Rev Recd Date: 2018-08-13

Available Online: 2018-08-27

Publish Date: 2018-12-01

Abstract

Abstract

Based on the theory of Galois rings of characteristic 4, a new class of quaternary sequences with period 2p² is established over Z₄ using generated cyclotomy, where p is an odd prime. The linear complexity of the new sequences is determined. Results show that the sequences have larger linear complexity and resist the attack by Berlekamp-Massey (B-M) algorithm. It is a good sequence from the viewpoint of cryptography.
- Stream ciphers,
- Quaternary sequences,
- Linear complexity,
- Generalized classes,
- Galois rings

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References(15)

References

GOLOMB S W and GONG Guang. Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar[M]. Cambridge: UK, Cambridge University Press, 2005: 174–175.

杜小妮, 王国辉, 魏万银. 周期为2p²的四阶二元广义分圆序列的线性复杂度[J]. 电子与信息学报, 2015, 37(10): 2490–2494 doi: 10.11999/JETT150180

DU Xiaoni, WANG Guohui, and WEI Wanyin. Linear complexity of binary generalized cyclotomic sequences of order four with period 2p²[J]. Journal of Electronics&Information Technology, 2015, 37(10): 2490–2494 doi: 10.11999/JETT150180

李瑞芳, 柯品惠. 一类新的周期为2pq的二元广义分圆序列的线性复杂度[J]. 电子与信息学报, 2014, 36(3): 650–654 doi: 10.3724/SP.J.1146.2013.00751

LI Ruifang and KE Pinhui. The linear complexity of a new class of generalized cyclotomic sequences with period 2pq[J]. Journal of Electronics&Information Technology, 2014, 36(3): 650–654 doi: 10.3724/SP.J.1146.2013.00751

ZHANG Jingwei and ZHAO Changan. The linear complexity of a class of binary sequences with period 2p[J]. Applicable Algebra in Engineering,Communication and Computing, 2015, 26(5): 475–491 doi: 10.1007/s00200-015-0261-8

MA Xiao, YAN Tongjiang, ZHANG Daode, et al. Linear complexity of some binary interleaved sequences of period 4N[J]. International Journal of Network Security, 2016, 18(2): 244–249 doi: 10.6633/IJNS.201603.18(2).06

EDEMSKIY V and PALVINSKIY A. The linear complexity of binary sequences of length 2p with optimal three-level autocorrelation[J]. Information Processing Letters, 2016, 116(2): 153–156 doi: 10.1016/j.ipl.2015.09.007

DU Xiaoni and CHEN Zhixiong. Linear complexity of quaternary sequences generated using generalized cyclotomic classes modulo 2p[J]. IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences, 2011, 94(5): 1214–1217 doi: 10.1587/transfun.E94.A.1214

CHEN Zhixiong. Linear complexity and trace representation of quaternary sequences over Z₄ based on generalized cyclotomic classes modulo[J]. Cryptography and Communications, 2017, 9(4): 445–458 doi: 10.1007/s12095-016-0185-6

EDEMSKIY V and IVANOV A. Linear complexity of quaternary sequences of length pq with low autocorrelation[J]. Journal of Computational and Applied Mathematics, 2014, 259B: 555–560 doi: 10.1016/j.cam.2013.08.003

EDEMSKIY V and IVANOV A. The linear complexity of balanced quaternary sequences with optimal autocorrelation value[J]. Cryptography and Communications, 2015, 7(4): 485–496 doi: 10.1007/s12095-015-0130-0

CHEN Zhixiong and EDEMSKIY V. Linear complexity of quaternary sequences over Z₄ derived from generalized cyclotomic classes modulo[OL]. arXiv preprint arXiv: 1603.05086, 2016.

IRELAND K and ROSEN M. A Classical Introduction to Modern Number Theory[M]. Germany: Springer Science & Business Media, 2013: 83–120.

UDAYA P and SIDDIQI M U. Generalized GMW quadriphase sequences satisfying the Welch bound with equality[J]. Applicable Algebra in Engineering,Communication and Computing, 2000, 10(3): 203–225 doi: 10.1007/s002000050125

WAN Zhexian. Finite Fields and Galois Rings[M]. Singapore, World Scientific Publishing Company, 2011: 23–25.

CUSICK T W, DING Gunsheng, and RENVALL A R. Stream Ciphers and Number Theory[M]. Dutch, Elsevier, 2004: 112–113.

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