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Home > Archive>Volume 13, Issue 8, 2002 >1368-1373
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Distribution of the Linear Complexities of Generalized Legendre Sequences
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    Abstract:

    In the paper, an estimation of distribution of linear complexities of generalized Legendre sequences is made. It is discovered that most of the generalized Legendre sequences have large linear complexities. A way is proposed to find the generalized Legendre sequence of the large linear complexity.

    Reference
    [1] Damgaard, I. On the randomness of Legendre and Jacobi sequences. In: Advance in Cryptology(CRYPTO'88). Berlin, Germany: Spring-Verlag, 1990. 163～172.
    [2] Ding, Cun-sheng, Helleseth, T., Shan, W. On the complexity of Legendre sequence. IEEE Transactions on IT, 1998,44(3): 1276～1278.
    [3] Bromfield, A.J., Piper, F.C. Linear recursion properties of unrelated binary sequences. Discrete Applied Mathematics, 1990,27(2): 187～193.
    [4] Dai, Zong-duo, Yang, Jun-hui, Gong, Guang, et al. On the linear complexity of generalized Legendre sequence. In: Helleseth, T., ed. Proceedings of the SETA2001. Spring-Verlag, 2001. 145～153.
    [5] Ding, Cun-sheng. The differential cryptanalysis and design of the natural stream ciphers. In: Preneel, B., ed., Fast Software Encryption. LNCS 809, Berlin: Springer-Verlag, 1994. 101～115.
    [6] Helleseth, T. Legendre sums and codes related to QR codes. Discrete applied Mathematics, 1992,35(1):107～113.
    [7] Hu, Yu-pu, Wei, Shi-ming, Xiao, Guo-zhen. On the linear complexity of generalized Legendre/Jacobi sequences. Acta Electronica Sinica, 2000,28(2):113～117 (in Chinese).
    [8] Lidl, R., Niederreiter, H. Finite Fields. In: Encyclopedia of Mathematics and Its Applications. Vol.20, Reading, MA: Addison-Wesley, 1983.
    [9] 胡予濮,魏仕民,肖国镇.广义Legendre序列和广义Jacobi序列的线性复杂度.电子学报,2000,28(2):113～117.
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王平,戴宗铎.广义Legendre序列线性复杂度的分布.软件学报,2002,13(8):1368-1373

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History
  • Received:September 03,2001
  • Revised:April 09,2002
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