Z4上周期為2p2的四元廣義分圓序列的線性復(fù)雜度
doi: 10.11999/JEIT180189
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西北師范大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院 ??蘭州 ??730070
基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61462077, 61772022),安徽省自然科學(xué)基金(1608085MF143),上海市自然科學(xué)基金(16ZR1411200)
Linear Complexity of Quaternary Sequences over Z4 Derived from Generalized Cyclotomic Classes Modulo 2p2
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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)
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摘要: 該文根據(jù)特征為4的Galois環(huán)理論,在Z4上利用廣義分圓構(gòu)造出一類新的周期為2p2(p為奇素?cái)?shù))的四元序列,并且給出了它的線性復(fù)雜度。結(jié)果表明,該序列具有良好的線性復(fù)雜度性質(zhì),能夠抗擊Berlekamp-Massey (B-M)算法的攻擊,是密碼學(xué)意義上性質(zhì)良好的偽隨機(jī)序列。
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關(guān)鍵詞:
- 流密碼 /
- 四元序列 /
- 線性復(fù)雜度 /
- 廣義分圓類 /
- Galois 環(huán)
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.-
Key words:
- Stream ciphers /
- Quaternary sequences /
- Linear complexity /
- Generalized classes /
- Galois rings
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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, 王國(guó)輝, 魏萬(wàn)銀. 周期為2p2的四階二元廣義分圓序列的線性復(fù)雜度[J]. 電子與信息學(xué)報(bào), 2015, 37(10): 2490–2494 doi: 10.11999/JETT150180DU 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. 一類新的周期為2pq的二元廣義分圓序列的線性復(fù)雜度[J]. 電子與信息學(xué)報(bào), 2014, 36(3): 650–654 doi: 10.3724/SP.J.1146.2013.00751LI 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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