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Dickson Pseudoprimes and Primality Testing

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Part of the book series:Lecture Notes in Computer Science ((LNCS,volume 547))

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Abstract

The paper gives a general definition for the concept of strong Dickson pseudoprimes which contains as special cases the Carmichael numbers and the strong Fibonacci pseudoprimes. Furthermore, we give necessary and sufficient conditions for two important classes of strong Dickson pseudoprimes and deduce some properties for their elements. A suggestion of how to improve a primality test by Baillie&Wagstaff concludes the paper.

This work peformed in part at the University of Klagenfurt was supported by the Forschungskommission of the University of Klagenfurt and by the Österreichischer Fonds zur Förderung der wissenschaftlichen Forschung under project no. P6174.

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References

  1. Chernick J.: On Fermat’s simple theorem. Bull.Amer.Math.Soc.45, 269–274 (1939).

    Article MATH MathSciNet  Google Scholar 

  2. Dubner H.: A New Method for Producing Large Carmichael Numbers. Math.Comp.53, No. 187, 411–414 (1989).

    Article MATH MathSciNet  Google Scholar 

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

    Article MATH MathSciNet  Google Scholar 

  4. 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 Science330, Springer-Verlag, New York-Berlin-Heidelberg, pp. 211–223, 1988.

    Google Scholar 

  5. Filipponi, P.: Table of Fibonacci Pseudoprimes to 108. Note Recensioni Notizie37, No. 1–2, 33–38 (1988).

    Google Scholar 

  6. Jaeschke, G.: Math.Comp.55, No. 191, 383–389 (1990).

    Article MATH MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  8. Lidl, R., MÜller, W.B.: Permutation polynomials in RSA-cryptosystems. Advances in Cryptology-Crypto’ 83 (ed. D. Chaum), New York, Plenum Press, pp. 293–301, 1984.

    Google Scholar 

  9. Lidl, R., MÜller, W.B.: Generalizations of the Fibonacci Pseudoprimes Test. To appear in Discrete Mathem.92 (1991).

    Google Scholar 

  10. Lidl, R., MÜller, W.B., Oswald A.: Some Remarks on Strong Fibonacci Pseudoprimes. Applicable Algebra in Engineering, Communication and Computing (AAECC)1, 59–65 (1990).

    Article MATH  Google Scholar 

  11. MÜller, W.B.: Polynomial Functions in Modern Cryptology. In: Contributions to General Algebra3, Teubner-Verlag, Stuttgart, pp. 7–32, 1985.

    Google Scholar 

  12. MÜller, W.B., NÖbauer R.: Cryptanalysis of the Dickson-scheme. In: Advances in Cryptology — Eurocrypt’85, Lecture Notes in Computer Science219, Springer-Verlag, New York-Berlin-Heidelberg, pp. 50–61, 1986.

    Google Scholar 

  13. NÖbauer, W.: Über die Fixpunkte der Dickson—Permutationen. Sb.d.Österr.Akad.-d.Wiss., math.-nat.Kl., Abt.II, Bd.193, 115–133 (1984).

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  15. Singmaster, D.: Some Lucas pseudoprimes. Abstracts Amer.Math.Soc.4, No.83T-10-146, p.197 (1983).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Klagenfurt, A-9022, Klagenfurt, Austria

    Winfried B. Müller

  2. School of Computing and Mathematics, Teesside Polytechnic, Middlesbrough, Cleveland, TS1 3BA, Great Britain

    Alan Oswald

Authors
  1. Winfried B. Müller

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  2. Alan Oswald

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Editor information

Editors and Affiliations

  1. Royal Holloway and Bedford New College, Univ. of London, Egham Hill, Surrey, TW20 0EX, UK

    Donald W. Davies

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© 1991 Springer-Verlag Berlin Heidelberg

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Müller, W.B., Oswald, A. (1991). Dickson Pseudoprimes and Primality Testing. In: Davies, D.W. (eds) Advances in Cryptology — EUROCRYPT ’91. EUROCRYPT 1991. Lecture Notes in Computer Science, vol 547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46416-6_45

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