Movatterモバイル変換

[0]ホーム
URL:

Skip to main content

Advertisement

Springer Nature Link
Log in

A key exchange system based on real quadratic fields Extended abstract

  • Conference paper
  • First Online:

Part of the book series:Lecture Notes in Computer Science ((LNCS,volume 435))

Included in the following conference series:

Abstract

In [3] Diffie and Hellman described a novel scheme by which two individuals could exchange a secret cryptographic key over a public channel. This scheme is based on the arithmetic in the multiplicative groupFx of a finite fieldF. It is secure because computing discrete logarithms in finite fields is a very hard problem. It has been noted subsequently by several authors (e.g. [1], [5], [6]) that any finite abelian groupG may be used to replaceFx in this scheme as long as the discrete logarithm problem inG is difficult.

Similar content being viewed by others

Keywords

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. J. Buchmann and H.C. Williams,A key exchange system based on imaginary quadratic fields, J. Cryptology1 (1988), 107–118.

    Article MATH MathSciNet  Google Scholar 

  2. H. Cohen and H.W. Lenstra Jr.,Heuristics on class groups of number fields, Number Theory (Nordwijkerhout, 1983), Lecture Notes in Math.1068, 33–62, Springer Verlag Berlin and New York, 1984.

    Chapter  Google Scholar 

  3. W. Diffie and M. Hellman,New directions in cryptography, IEEE Trans. Inform. Theory22 (1976), 472–492.

    Article MathSciNet  Google Scholar 

  4. P. Kaplan,Sur le 2-groupe des classes d’idéaux des corps quadratiques, J. Reine Angew. Math.283/284 (1976), 313–363.

    Google Scholar 

  5. N. Koblitz,Elliptic curve cryptosystems, Math. Comp.48 (1987), 203–209.

    Article MATH MathSciNet  Google Scholar 

  6. K.S. McCurley,A key distribution system equivalent to factoring, J. Cryptology1 (1988), 95–105.

    Article MATH MathSciNet  Google Scholar 

  7. R.A. Mollin and H.C. Williams,Computation of the class number of a real quadratic field, preprint (1988).

    Google Scholar 

  8. R.J. Schoof,Quadratic fields and factorization in Computational methods in number theory, H.W. Lenstra Jr. and R. Tijdeman, eds., Math. Centrum Tracts155, Part II, Amsterdam (1983), 235–286.

    Google Scholar 

  9. D. Shanks,The infrastructure of a real quadratic field and its applications, Proc. 1972 Number Theory Conf., Boulder, Colorado, (1973), 217–224.

    Google Scholar 

  10. D. Shanks,Systematic examination of Littlewood’s bounds on L(1,χ), Proc. Sympos. Pure Math.24, AMS Providence RI (1973), 267–283.

    Google Scholar 

  11. H.C. Williams,Continued fractions and number-theoretic computations, Rocky Mountain J. Math.15 (1985), 621–655.

    Article MATH MathSciNet  Google Scholar 

  12. H.C. Williams and M.C. Wunderlich,On the parallel generation of the residues for the continued fraction factoring algorithm, Math. Comp.48 (1987), 405–423.

    Article MATH MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. FB 10-Informatik, Universität des Saarlandes, 6600, Saarbrücken, West Germany

    Johannes A. Buchmann

  2. Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada, R3T2N2

    Hugh C. Williams

Authors
  1. Johannes A. Buchmann

    You can also search for this author inPubMed Google Scholar

  2. Hugh C. Williams

    You can also search for this author inPubMed Google Scholar

Editor information

Editors and Affiliations

  1. Département IRO, Université de Montréal, C.R 6128, Succursale “A”, Montréal, Québec, Canada, H3C 3J7

    Gilles Brassard

Rights and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Buchmann, J.A., Williams, H.C. (1990). A key exchange system based on real quadratic fields Extended abstract. In: Brassard, G. (eds) Advances in Cryptology — CRYPTO’ 89 Proceedings. CRYPTO 1989. Lecture Notes in Computer Science, vol 435. Springer, New York, NY. https://doi.org/10.1007/0-387-34805-0_31

Download citation

Publish with us

[8]ページ先頭
©2009-2025 Movatter.jp