Skip to main content
Log in

A note on the crosscorrelation of maximal length FCSR sequences

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

In this note it is shown that if the connection integers of two maximal length FCSR sequences have a common prime factor, then any crosscorrelation between them can be converted into some autocorrelation of the sequence with smaller period.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Klapper A., Goresky M.: 2-Adic shift registers. In: Fast Software Encryption, Cambridge Security Workshop. Lecture Notes in Computer Science, vol. 809, pp. 174–178. Springer-Verlag, New York (1993).

  2. Klapper A., Goresky M.: Feedback shift registers, 2-adic span, and combiners with memory. J. Cryptol. 10, 111–147 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Qi W.F., Xu H.: Partial period distribution of FCSR sequences. IEEE Trans. Inform. Theory 49(3), 761–765 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Seo C., Lee S., Sung Y., Han K., Kim S.: A lower bound on the linear span of an FCSR. IEEE Trans. Inform. Theory 46(2), 691–693 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Goresky M., Klapper A.: Arithmetic crosscorrelations of feedback with carry shift register sequences. IEEE Trans. Inform. Theory 43(4), 1342–1345 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Xu H., Qi W.F.: Autocorrelations of maximum period FCSR sequences. SIAM J. Discrete Math. 20(3), 568–577 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Arnault F., Berger T.P.: Design and properties of a new pseudorandom generator based on a filtered FCSR automaton. IEEE Trans. Inform. Theory 54(11), 1374–1383 (2005)

    Google Scholar 

  8. Arnault F., Berger T.P., Lauradoux C.: Update on F-FSCR stream cipher, ECRYPT Stream Cipher Project Report 2006/025 (2006) http://www.ecrypt.eu.org/stream.

  9. Dai Z.D.: Binary sequences derived from ML-sequences over rings I: periods and minimal polynomials. J. Cryptol. 5(4), 193–207 (1992)

    Article  MATH  Google Scholar 

  10. Huang M.Q., Dai Z.D.: Projective maps of linear recurring sequences with maximal p-adic periods. Fibonacci Quart. 30(2), 139–143 (1992)

    MATH  MathSciNet  Google Scholar 

  11. Zhu X.Y., Qi W.F.: Compression mappings on primitive sequences over \({\mathbf{Z}/(p^{e})}\) . IEEE Trans. Inform. Theory 50(10), 2442–2448 (2004)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wen-Feng Qi.

Additional information

Communicated by H. Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tian, T., Qi, WF. A note on the crosscorrelation of maximal length FCSR sequences. Des. Codes Cryptogr. 51, 1–8 (2009). https://doi.org/10.1007/s10623-008-9238-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-008-9238-y

Keywords

Mathematics Subject Classification (2000)

Navigation