一類新的周期為的二元廣義分圓序列的線性復雜度

李瑞芳 柯品惠

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李瑞芳 柯品惠*

(福建師范大學網絡安全與密碼技術福建省重點實驗室 福州 350007)

密碼學；有限域；廣義分圓序列；線性復雜度

1 引言

一條序列的線性復雜度定義為生成該序列的最短的線性移位寄存器的長度。在密碼學等相關領域的應用中，偽隨機序列必須具有高的線性復雜度[1,2]。從安全的角度講，一條好的序列往往要求它的線性復雜度必須不小于其周期長度的一半。

易驗證，

3 線性復雜度

本節將計算第2節定義的廣義分圓序列的線性復雜度，為此，需要如下引理。

定義如式(5)輔助多項式：

則

由于不同專家之間的意見不同，需要將專家的意見作為證據進行證據融合。融合證據之前，運用式(5)—式(7)計算折扣后的證據BPA,再運用式(8)對各證據的BPA進行融合。

由式(4)，序列的線性復雜度為

證畢

記

綜上，可知結論成立。 證畢

類似于引理4，容易證明引理5。

及

由引理2得，

證畢

4 結論

[1] Golomb S W and Gong G. Signal Design for Good Correlation: For Wireless Communications, Cryptography and Radar Applications[M]. Cambridge: UK, Cambridge University Press, 2005: 174-175.

[2] Cusick T, Ding C, and Renvall A. Stream Ciphers and Number Theory[M]. Amsterdam: The Netherlands, North- Holland Mathematical Library 55, 1998: 198-212.

[3] Ding C and Helleseth T. Generalized cyclotomy and its applications[J]., 1999, (4): 467-474.

[4] Ding C, Hellseth T, and Shan W. On the linear complexity of Legendre sequences[J]., 1998, 44(3): 1276-1278.

[5] Kim Y J, Jin S Y, and Song H Y. Linear complexity and autocorrelation of prime cube sequences[J]., 2007, 4851: 188-197.

[6] Kim Y J and Song H Y. Linear complexity of prime n-square sequences[C]. IEEE International Symposium on Information Theory, Toronto, Canada, 2008: 2405-2408.

[7] Yan T, Sun R, and Xiao G. Autocorrelation and linear complexity of the new generalized cyclotomic sequences[J]., 2007, E90-A: 857-864.

[8] Yan T, Li S, and Xiao G. On the linear complexity of generalized cyclotomic sequences with the periodp[J].2008, (21): 187-193.

[9] Edemskiy V. About computation of the linear complexity of generalized cyclotomic sequences with periodp+1[J]., 2011, 61(3): 251-260.

[10] Zhang J W, Zhao C A, and Ma X. Linear complexity of generalized cyclotomic binary sequences of length 2p[J]., 2010, (21): 93-108.

[11] Ke P H, Zhang J, and Zhang S Y. On the linear complexity and the autocorrelation of generalized cyclotomic binary sequences of length 2p[J].2012, 67(3): 325-339.

[12] Ke P H and Zhang S Y. New classes of quaternary cyclotomic sequence of length 2pwith high linear complexity[J]., 2012, 12(16): 646-650.

[13] Hu L Q, Yue Q, and Wang M H. The linear complexity of Whiteman’s generalized cyclotomic sequences of periodp+1q+1[J]., 2012, 58(8): 5534-5542.

[14] Du X N and Chen Z X. A generalization of the Hall’s sixtic residue sequences[J]., 2013, 222: 784-794.

[15] Chang Z L and Li D D. On the linear complexity of generalized cyclotomic binary sequences of length 2[J]., 2013, DOI: 10.1002/cpe.3052.

李瑞芳： 女，1988年生，碩士生，研究方向為序列設計.

柯品惠： 男，1978年生，副教授，主要研究方向包括序列設計、現代密碼學中的布爾函數.

Li Rui-fang Ke Pin-hui*

(,,350007,)

Crpytography; Finite fields; Generalized cyclotomic sequence; Linear complexity

TN918.1

A

1009-5896(2014)03-0650-05

10.3724/SP.J.1146.2013.00751

2013-05-27收到，2013-08-12改回

國家自然科學基金(61102093)資助課題

柯品惠 keph@fjnu.edu.cn