Abstract
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.
W. Diffie, M. Hellman, New directions in cryptography, IEEE Trans. Inform. Theory, vol. 22, 1976.
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).
A. J. Stephens, H. C. Williams, Some computational results on a problem concerning powerful numbers, Math. of Comp. vol. 50, no. 182, April 1988.
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.
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© 1991 Springer-Verlag Berlin Heidelberg
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Scheidler, R., Buchmann, J.A., Williams, H.C. (1991). Implementation of a Key Exchange Protocol Using Real Quadratic Fields. In: Damgård, I.B. (eds) Advances in Cryptology — EUROCRYPT ’90. EUROCRYPT 1990. Lecture Notes in Computer Science, vol 473. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46877-3_9
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DOI: https://doi.org/10.1007/3-540-46877-3_9
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