Skip to main content

Periodicity and Distribution Properties of Combined FCSR Sequences

  • Conference paper
Sequences and Their Applications – SETA 2006 (SETA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4086))

Included in the following conference series:

  • 1284 Accesses

Abstract

This is a study of some of the elementary statistical properties of the bitwise exclusive or of two maximum period feedback with carry shift register sequences. We obtain conditions under which the resulting sequences has the maximum possible period, and we obtain bounds on the variation in the distribution of blocks of a fixed length. This may lead to improved design of stream ciphers using FCSRs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Blum, L., Blum, M., Shub, M.: A simple unpredictable pseudorandom number generator. SIAM J. Comput. 15, 364–383 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dickson, L.E.: History of the Theory of Numbers, Chelsea, New York, vol. 1 (1950)

    Google Scholar 

  3. Gauss, C.F.: Disquisitiones Arithmeticae, Leipzig, 1801, English translation, Yale, New haven (1966)

    Google Scholar 

  4. Klapper, A., Goresky, M.: 2-adic shift registers. In: Anderson, R. (ed.) FSE 1993. LNCS, vol. 809, pp. 174–178. Springer, Heidelberg (1994)

    Google Scholar 

  5. Klapper, A., Goresky, M.: Feedback Shift Registers, Combiners with Memory, and 2-Adic Span. Journal of Cryptology 10, 111–147 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Klapper, A., Goresky, M.: Arithmetic crosscorrelation of feedback with carry shift registers. IEEE Trans. Info. Theory 43, 1342–1345 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Mandelbaum, D.: Arithmetic codes with large distance. IEEE Trans. Info. Theory IT-13, 237–242 (1967)

    Article  Google Scholar 

  8. Rueppel, R.: Analysis and Design of Stream Ciphers. Springer, New York (1986)

    MATH  Google Scholar 

  9. Schneier, B.: Applied Cryptography. John Wiley & Sons, New York (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Goresky, M., Klapper, A. (2006). Periodicity and Distribution Properties of Combined FCSR Sequences. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_29

Download citation

  • DOI: https://doi.org/10.1007/11863854_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44523-4

  • Online ISBN: 978-3-540-44524-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics