Abstract
This paper contributes to the stability of linear complexity of a binary periodic Jacobi sequence. By employing a pair of reference sequences, we prove that the linear complexity of a binary Jacobi sequence is unstable, namely, by changing its few bits in one-period length, the linear complexity of the modified sequences will become far less than the required value.
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References
Ding C, Xiao G, Shan W. The stability theory of stream ciphers [C] // Lecture Notes in Computer Science (LNCS 561). Berlin: Springer-Verlag, 1991.
Ding C. Binary cyclotomic generators, fast software encryption [C] //Lecture Notes in Computer Science (LNCS 1008). Berlin: Springer-Berlin, 1995: 20–60.
Ding C. Linear complexity of generalized cyclotomic binary sequence of order 2 [J]. Finite Fields and Their Applications, 1997,(3): 159–174.
Ding C. Autocorrelation values of generalized cyclotomic sequences of order two [J]. IEEE Transactions on Information Theory, 1998, 44(5): 1699–1702.
Dai Z, Gong G, Song H. A trace representation of binary Jacobi sequences [J]. Discrete Mathematics, 2009, 309(6): 1517–1527.
Du X, Chen Z. Trace representations of generalized cyclotomic sequences of length pq with arbitrary order [J]. Chinese Journal of Electronics, 2009, 18(3): 460–464.
Brandstatter N, Winterhof A. Some notes on the twoprime generator [J]. IEEE Transactions on Information Theory, 2005, 51(10): 3654–3657.
Jensen J M, Jensen H E, Høholdt T. The merit factor of binary sequences related to difference sets [J]. IEEE Transactions on Information Theory, 1991, 37(3): 617–626.
Bai E, Liu X, Xiao G. Linear complexity of new generalized cyclotomic sequences of order two of length pq [J]. IEEE Transactions on Information Theory, 2005, 51(5): 1849–1853.
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Foundation item: Supported by the National Natural Science Foundation of China (61170319, 61063041), the Natural Science Fund of Shandong Province (ZR2010FM017), the China Postdoctoral Science Foundation Funded Project( 119103S148), and the Fundamental Research Funds for the Central Universities( 11CX04056A, 10CX04038A)
Biography: YAN Tongjiang, male, Ph.D., Associate professor, research direction: sequences design, stream cipher and semigroup.
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Yan, T., Sun, Y. Linear complexity problem of binary Jacobi sequence. Wuhan Univ. J. Nat. Sci. 17, 481–484 (2012). https://doi.org/10.1007/s11859-012-0874-8
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DOI: https://doi.org/10.1007/s11859-012-0874-8