Advertisement

Linear Complexity and Autocorrelation of Prime Cube Sequences

  • Young-Joon Kim
  • Seok-Yong Jin
  • Hong-Yeop Song
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4851)

Abstract

We review a binary sequence based on the generalized cyclotomy of order 2 with respect to p 3, where p is an odd prime. Linear complexities, minimal polynomials and autocorrelation of these sequences are computed.

Keywords

Binary Sequence Linear Complexity Fourth Term Minimal Polynomial Stream Cipher 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ding, C., Helleseth, T.: New Generalized Cyclotomy and Its Application. Finite Fields and Their Applications 4, 140–166 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Burton, D.M.: Elementary Number Theory, 4th edn. McGraw-Hill, New York (1998)zbMATHGoogle Scholar
  3. 3.
    Golomb, S.W.: Shift Register Sequences, Revised edn. Aegean Park Press, Laguna Hills (1982)Google Scholar
  4. 4.
    Ding, C.: Linear Complexity of Some Generalized Cyclotomic Sequences. Int. J. Algebra and Computation 8, 431–442 (1998)zbMATHCrossRefGoogle Scholar
  5. 5.
    Park, Y.H., Hong, D., Chun, E.: On the Linear Complexity of Some Generalized Cyclotomic Sequences. Int. J. Algebra and Computation 14, 431–439 (2004)zbMATHCrossRefGoogle Scholar
  6. 6.
    Cusick, T., Ding, C., Renvall, A.: Stream Ciphers and Number Theory. Elservier Science, Amsterdam (1998)zbMATHCrossRefGoogle Scholar
  7. 7.
    Yan, T., Sun, R., Xiao, G.: Autocorrelation and Linear Complexity of the New Generalized Cyclotomic Sequences. IEICE Trans. Fundamentals E90-A, 857–864 (2007)CrossRefGoogle Scholar
  8. 8.
    Bai, E., Liu, X., Xiao, G.: Linear Complexity of New Generalized Cyclotomic Sequences of Order Two of Length pq. IEEE Trans. Inform. Theory 51, 1849–1853 (2005)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Young-Joon Kim
    • 1
  • Seok-Yong Jin
    • 1
  • Hong-Yeop Song
    • 1
  1. 1.Department of Electrical and Electronic Engineering, Yonsei University, Seoul, 121-749Korea

Personalised recommendations