一類新的周期為2pm的q階二元廣義分圓序列的線性復(fù)雜度
doi: 10.11999/JEIT180884 cstr: 32379.14.JEIT180884
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西安建筑科技大學(xué)理學(xué)院 西安 710055
基金項(xiàng)目: 國(guó)家自然科學(xué)基金(11471255)，西安建筑科技大學(xué)自然科學(xué)專項(xiàng)(1609718034)，西安建筑科技大學(xué)人才基金(RC1338)
The Linear Complexity of a New Class of Generalized Cyclotomic Sequence of Order q with Period 2pm
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School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China
Funds: The National Natural Science Foundation of China (11471255), The Natural Science Project of Xi’an University of Architecture and Technology (1609718034), The Talent Fund of Xi’an University of Architecture and Technology (RC1338)
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摘要: 該文基于Ding-廣義分圓理論，將周期為
$ 2{p^m}$ ($ p$ 為奇素?cái)?shù)，$ m$ 為正整數(shù))廣義分圓序列的研究推廣到任意素?cái)?shù)階情形，構(gòu)造了一類新序列。通過(guò)數(shù)論方法分析多項(xiàng)式廣義分圓類，確定并計(jì)算線性復(fù)雜度與序列的2次剩余類和2次非剩余類的劃分緊密相關(guān)。結(jié)果表明該類序列的線性復(fù)雜度遠(yuǎn)遠(yuǎn)大于周期的一半，能抗擊應(yīng)用Berlekamp-Massey(B-M)算法的安全攻擊，是密碼學(xué)意義上性質(zhì)良好的偽隨機(jī)序列。-
關(guān)鍵詞:
- 廣義分圓序列 /
- 線性復(fù)雜度 /
- 2次剩余類 /
- Berlekamp-Massey算法
Abstract: Based on the theory of Ding - generalized circle, a new class of generalized cyclotomic sequences of$ 2{p^m}$ ($ p$ odd prime and m>1) with arbitrary prime order is constructed in this paper. The polynomial cyclotomic classes are analysed by algebra number theory method. Moreover, the linear complexity of the new sequences are determined, which losely related to the division of quadratic residual classes and quadratic non-residual classes. Results show that the linear complexity of this kind of sequence is much larger than half of the period, hence, can fight Berlekamp-Massey’s security application attack that is a pseudo-random sequence with good properties in the sense of cryptography. -
GOLOMB S W and GONG Guang. Signal Design for Good Correlation: For Wireless Communication, Cryptography and Radar[M]. Cambridge: Cambridge University Press, 2005: 174–175. DING Cunsheng. Linear complexity of generalized cyclotomic binary sequences of order 2[J]. Finite Fields and Their Applications, 1997, 3(2): 159–174. doi: 10.1006/ffta.1997.0181 DING Cunsheng, HESSESETH T, and SHAN Weijuan. On the linear complexity of Legendre sequences[J]. IEEE Transactions on Information Theory, 1998, 44(3): 1276–1278. doi: 10.1109/18.669398 BAI Enjian, LIU Xiaojuan, and XIAO Guozhen. Linear complexity of new generalized cyclotomic sequences of order two of length pq[J]. IEEE Transactions on Information Theory, 2005, 51(5): 1849–1853. doi: 10.1109/TIT.2005.846450 YAN Tongjiang, LI Shengqiang, and XIAO Guozhen. On the linear complexity of generalized cyclotomic sequences with the period p m[J]. Applied Mathematics Letters, 2008, 21(2): 187–193. doi: 10.1016/j.aml.2007.03.011 DU Xiaoni, YAN Tongjiang, and XIAO Guozhen. Trace representation of some generalized cyclotomic sequences of length pq[J]. Information Sciences, 2008, 178(16): 3307–3316. doi: 10.1016/j.ins.2007.11.023 魏萬(wàn)銀, 杜小妮, 王國(guó)輝. 周期為2pq的四元序列線性復(fù)雜度研究[J]. 計(jì)算機(jī)工程, 2016, 42(3): 161–164. doi: 10.3969/j.issn.1000-3428.2016.03.029WEI Wanyin, DU Xiaoni, and WANG Guohui. Research on linear complexity of quaternary sequences with period 2pq[J]. Computer Engineering, 2016, 42(3): 161–164. doi: 10.3969/j.issn.1000-3428.2016.03.029 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/JEIT150180DU 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/JEIT150180 HU Liqin, YU Qin, and WANG Minhong. The linear complexity of Whiteman’s generalized cyclotomic sequences of period $ {p^{m + 1}}{q^{n + 1}}$ [J]. IEEE Transactions on Information Theory, 2012, 58(8): 5534–5543. doi: 10.1109/TIT.2012.2196254ZHANG Jingwei, ZHAO Chang’an, and MA Xiao. Linear complexity of generalized cyclotomic binary sequences of length 2p m[J]. Applicable Algebra in Engineering, Communication and Computing, 2010, 21(2): 93–108. doi: 10.1007/s00200-009-0116-2 TAN Lin, XU Hong, and QI Wenfeng. Remarks on the generalized cyclotomic sequences of length 2p m[J]. Applicable Algebra in Engineering, Communication and Computing, 2012, 23(5/6): 221–232. doi: 10.1007/s00200-012-0177-5 KE Pinhui, ZHANG Jie, and ZHANG Shengyuan. On the linear complexity and the autocorrelation of generalized cyclotomic binary sequences of length 2p n[J]. Designs, Codes and Cryptography, 2013, 67(3): 325–339. doi: 10.1007/s10623-012-9610-9 EDEMSKIY V and ANTONOVA O. The linear complexity of generalized cyclotomic sequences with period 2p n[J]. Applicable Algebra in Engineering, Communication and Computing, 2014, 25(3): 213–223. doi: 10.1007/s00200-014-0223-6 EDEMSKIY V. About computation of the linear complexity of generalized cyclotomic sequences with period p n+1[J]. Designs, Codes and Cryptography, 2011, 61(3): 251–260. doi: 10.1007/s10623-010-9474-9 劉龍飛, 楊凱, 楊曉元. 新的周期為p m的GF(h)上廣義割圓序列的線性復(fù)雜度[J]. 通信學(xué)報(bào), 2017, 38(9): 39–45. doi: 10.11959/j.issn.1000-436x.2017181LIU Longfei, YANG Kai, and YANG Xiaoyuan. On the linear complexity of a new generalized cyclotomic sequence with length p m over GF(h)[J]. Journal on Communications, 2017, 38(9): 39–45. doi: 10.11959/j.issn.1000-436x.2017181 XIAO Zibi, ZENG Xiangyong, LI Chunlei, et al. New generalized cyclotomic binary sequences of period p2[J]. Designs, Codes and Cryptography, 2018, 86(7): 1483–1497. doi: 10.1007/s10623-017-0408-7 -
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