Skip to main content
SpringerLink
Log in

Multisequence Synthesis over an Integral Domain

  • Conference paper
  • First Online:
Cryptography and Lattices (CaLC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2146))

Included in the following conference series:

Abstract

We first give an extension of F[x]-lattice basis reduction algorithm to the polynomial ring R[x] where F is a field and R an arbitrary integral domain. So a new algorithm is presented for synthesizing minimum length linear recurrence (or minimal polynomials) for the given multiple sequences over R. Its computational complexity is O(N 2) multiplications in R where N is the length of each sequence. A necessary and sufficient conditions for the uniqueness of minimal polynomials are given. The set of all minimal polynomials is also described.

Research supported by NSF under grants No. 19931010 and G 1999035803.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fitzpatrick, P., Norton, G. H.: The Berlekamp-Massey algorithm and linear recurring sequences over a factorial domain. AAECC, 6 (1995) 309–323

    Article  MATH  MathSciNet  Google Scholar 

  2. Lu, P. Z., Liu, M. L.: Gröbner basis for characteristic ideal of linear recurrence sequence over UFD. Science in China (Series A), vol. 28, No. 6. 508–519 (1998)

    Google Scholar 

  3. Norton, G. H.: On shortest linear recurrences. J. Symb. Comp. 27 (1999) 325–349

    Article  MATH  MathSciNet  Google Scholar 

  4. Schmidt, W. M.: Construction and estimation of bases in function fields. J. Number Theory 39, no. 2, 181–224 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  5. Wang, L. P., Zhu, Y. F.: F[x]-lattice basis reduction algorithm and multisequence synthesis. Science in China, in press

    Google Scholar 

  6. Lenstra, A. K., Lenstra, H. W., Lovasz, L.: Factoring polynomials with rational coefficients. Math. Ann., vol. 261 (1982) 515–534

    Article  MATH  MathSciNet  Google Scholar 

  7. Lagarias, J. C., Odlyzko, A. M.: Soluting low density subset problems. Pro. 24th Annual IEEE Symp. on Found of Comp. Science (1983) 1–10

    Google Scholar 

  8. Coppersmith, D.: Small solutions to polynomial equations and low exponent RSA vulnerabilities. Journal of Cryptology 10 (1997) 233–260

    Article  MATH  MathSciNet  Google Scholar 

  9. Berlekamp, E. R.: Algebraic Coding Theory. New York: McGrawHill (1968)

    MATH  Google Scholar 

  10. Massey, J. L.: Shift-register synthesis and BCH decoding. IEEE Trans. Inform. Theory, vol. IT-15, no. 1, 122–127 (1969)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Graduate School, University of Science and Technology of China, Beijing, 100039, China

    Li-ping Wang

  2. Department of Network Engineering, Information Engineering University, Zhengzhou, 450002, China

    Yue-fei Zhu

Authors
  1. Li-ping Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yue-fei Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mathematics Department, Brown University, Box 1917, Providence, RI, 02912, USA

    Joseph H. Silverman

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, Lp., Zhu, Yf. (2001). Multisequence Synthesis over an Integral Domain. In: Silverman, J.H. (eds) Cryptography and Lattices. CaLC 2001. Lecture Notes in Computer Science, vol 2146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44670-2_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-44670-2_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42488-8

  • Online ISBN: 978-3-540-44670-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation