Skip to main content

A note on strong Fibonacci pseudoprimes

  • Section 8 Theory
  • Conference paper
  • First Online:
Advances in Cryptology — AUSCRYPT '90 (AUSCRYPT 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 453))

Included in the following conference series:

Abstract

After summarizing some results on pseudoprimes, a characterization is presented of Fibonacci pseudoprimes of the b th kind for all integers b. Subsequently, some generalizations of the concept of strong pseudoprimes are established.

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.

References

  1. Baillie, R., Wagstaff Jr., S.S.: Lucas pseudoprimes. Math.of Comp. 35, 1391–1417 (1980).

    Google Scholar 

  2. Dickson, L.: The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group I. Ann.of Math. 11, 65–120 (1896).

    Google Scholar 

  3. Di Porto, A., Filipponi, P.: A Probabilistic Primality Test Based on the Properties of Certain Generalized Lucas Numbers. In: Advances in Cryptology — Eurocrypt'88, Lecture Notes in Computer Science 330, Springer-Verlag, New York-Berlin-Heidelberg, pp. 211–223, 1988.

    Google Scholar 

  4. Di Porto, A., Filipponi, P.: Extended Abstract, Eurocrypt'89, Houthalen (Belgium), April 10–13, 1989.

    Google Scholar 

  5. Filipponi, P.: Table of Fibonacci Pseudoprimes to 108. Note Recensioni Notizie 37, no. 1–2, 33–38 (1988).

    Google Scholar 

  6. Koblitz, N.: A Course in Number Theory and Cryptography. Springer-Verlag, New York-Berlin-Heidelberg, 1987.

    Google Scholar 

  7. Lidl, R.: Tschebyscheffpolynome in mehreren Variablen. J.reine angew.Math. 273, 178–198 (1975).

    Google Scholar 

  8. Lidl, R., Müller, W.B.: Generalizations of the Fibonacci Pseudoprimes Test. To appear.

    Google Scholar 

  9. Lidl, R., Müller, W.B., Oswald, A.: Some Remarks on Strong Fibonacci Pseudoprimes. To appear in Applicable Algebra in Engineering, Communication and Computer Science 1 (1990).

    Google Scholar 

  10. Lidl, R., Niederreiter, H.: Finite Fields. Addison Wesley, Reading, 1983. (Now published by Cambridge University Press, Cambridge.)

    Google Scholar 

  11. Lidl, R., Wells, C.: Chebyshev polynomials in several variables. J.reine angew.Math. 255, 104–111 (1972).

    Google Scholar 

  12. Nöbauer, R.: Über die Fixpunkte einer Klasse von Dickson-Permutationen. Sb.d.Österr.Akad.d.Wiss., math.-nat.Kl., Abt.II, Bd. 193, 521–547 (1984).

    Google Scholar 

  13. Ribenboim, P.: The Book of Prime Number Records. Springer-Verlag, New York-Berlin-Heidelberg, 1988.

    Google Scholar 

  14. Von zur Gathen, J.:Testing permutation polynomials. Proc. 30 Annual IEEE Symp. Foundations of Computer Science, pages 88–92, Research Triangle Park, NC, 1989

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Jennifer Seberry Josef Pieprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lidl, R., Müller, W.B. (1990). A note on strong Fibonacci pseudoprimes. In: Seberry, J., Pieprzyk, J. (eds) Advances in Cryptology — AUSCRYPT '90. AUSCRYPT 1990. Lecture Notes in Computer Science, vol 453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030371

Download citation

  • DOI: https://doi.org/10.1007/BFb0030371

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53000-8

  • Online ISBN: 978-3-540-46297-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics