Implementation of a Key Exchange Protocol Using Real Quadratic Fields

Extended Abstract
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 473)


In [1] Buchmann and Williams introduced a key exchange protocol which is based on the Diffie-Hellman protocol (see [2]). However, instead of employing arithmetic in the multiplicative group F* of a finite field F (or any finite Abelian group G), it uses a finite subset of an infinite Abelian group which itself is not a subgroup, namely the set of reduced principal ideals in a real quadratic field. As the authors presented the scheme and its security without analyzing its actual implementation, we will here discuss the algorithms required for implementing the protocol.


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    J. A. Buchmann, H. C. Williams, A key exchange system based on real quadratic fields, extended abstract, to appear in: Proceedings of CRYPTO’ 89.Google Scholar
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    W. Diffie, M. Hellman, New directions in cryptography, IEEE Trans. Inform. Theory, vol. 22, 1976.Google Scholar
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    R. A. Mollin, H. C. Williams, Computation of the class number of a real quadratic field, to appear in: Advances in the Theory of Computation and Computational Mathematics (1987).Google Scholar
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    A. J. Stephens, H. C. Williams, Some computational results on a problem concerning powerful numbers, Math. of Comp. vol. 50, no. 182, April 1988.Google Scholar
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    H. C. Williams, M. C. Wunderlich, On the parallel generation of the residues for the continued fraction factoring algorithm, Math. of Comp. vol. 48, no. 177, January 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of ManitobaWinnipegCanada
  2. 2.FB-10 InformatikUniversität des SaarlandesSaarbrückenWest Germany

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