LIANG Wanwan, ZENG Xiangyong, XU Yunge, “The Periods of a Class of Nonlinear Feedback Shift Register Sequences,” Chinese Journal of Electronics, vol. 25, no. 2, pp. 296-303, 2016, doi: 10.1049/cje.2016.03.016
Citation: LIANG Wanwan, ZENG Xiangyong, XU Yunge, “The Periods of a Class of Nonlinear Feedback Shift Register Sequences,” Chinese Journal of Electronics, vol. 25, no. 2, pp. 296-303, 2016, doi: 10.1049/cje.2016.03.016

The Periods of a Class of Nonlinear Feedback Shift Register Sequences

doi: 10.1049/cje.2016.03.016
Funds:  This work is supported by the National Natural Science Foundation of China (No.61472120).
More Information
  • Corresponding author: ZENG Xiangyong (corresponding author) was born in Hubei Province, China, in 1973. He received the M.S and Ph.D. degrees in Beijing Normal University. Since 2009, he has been a professor of Hubei University. He serves as an associate editor for the Springer journal Cryptography and Communications, Discrete Structures, Boolean Functions and Sequences. His research interests include cryptography, sequence and coding theory. (Email:xzeng@hubu.edu.cn)
  • Received Date: 2014-11-13
  • Rev Recd Date: 2015-03-10
  • Publish Date: 2016-03-10
  • In this paper, we discuss a class of n-stage Nonlinear feedback shift registers (NFSRs). Applying the knowledge of algebra, the least periods of the sequences generated by these NFSRs with symmetric feedback functions can be characterized. This approach simplifies the problem of determining the periods of the NFSR sequences and it generalizes some Cheng's results.
  • loading
  • M. Hell, T. Johansson, A. Maximov, et al., "The Grain family of stream ciphers", Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany, Vol.4986, pp.179-190, 2008.
    A.J. Menezes, P.C. Van Oorschot and S.A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, USA, 1997.
    S.W. Golomb, Shift Register Sequences, Aegean Park Press, New York, USA, 1982.
    C.Y. Li, X.Y. Zeng, T. Helleseth, et al., "The properties of a class of linear FSRs and their applications to the construction of nonlinear FSRs", IEEE Transactions on Information Theory, Vol.60, No.5, pp.3052-3061, 2014.
    S.X. Zhu, "An algorithm for generating de Bruijn sequences by raising elements ", Journal of Electronics, Vol.22, No.1, pp.68-72, 2000. (in Chinese)
    S.X. Zhu and L. Sun, "An algorithm for generating feedback functions of k-ary de Bruijn sequences by raising stage", Acta Electronica Sinica, Vol.34, No.6, pp.1066-1068, 2006. (in Chinese)
    C. Cannière and B. Preneel, "Trivium", Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany, Vol.4986, pp.244-266, 2008.
    S. Babbage and M. Dodd, "The MICKY stream ciphers", Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany, Vol.4986, pp.191-209, 2008.
    K. Kjeldsen, " On the cycle structure of a set of nonlinear shift registers with symmetric feedback functions", Journal of Combinatorial Theory, Vol.A, No.20, pp.154-169, 1976.
    J. Søreng, "The periods of the sequences generated by some symmetric shift registers", Journal of Combinatorial Theory, Vol.A, No.21, pp.164-187, 1976.
    J. Søreng, "Symmetric shift registers", Pacific Journal of Mathematics, Vol.85, No.1, pp.201-229, 1979.
    J. Søreng, "Symmetric shift registers, Part 2", Pacific Journal of Mathematics, Vol.98, No.1, pp.203-234, 1982.
    U. Cheng, "On the cycle structure of certain classes of nonlinear shift registers", Journal of Combinatorial Theory, Vol.A, No.37, pp.61-68, 1984.
    Z.X.Wang, H. Xu and W.F. Qi, "On the cycle structure of some nonlinear feedback shift registers", Chinese Journal of Electronics, Vol.23, No.4, pp.801-804, 2014.
    K. Hoffman and R. Kunze, Linear Algebra (2nd ed), Prentice-Hall, Englewood Cliffs, New Jery, 1971.
    D. Serre, Matrices: Theory and Applications, translated from the 2001 French original. Graduate Texts in Mathematics 216, Dunod, Paris, 2001.
    R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, England, 1997.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (575) PDF downloads(655) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return