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The Equivalence between the DHP and DLP for Elliptic Curves Used in Practical Applications

Published online by Cambridge University Press:  01 February 2010

A. Muzereau
Affiliation:
Ecole Nationale Supérieure d'Informatique et de Mathématiques Appliquées de Grenoble Rue de la Passerelle, 481, Domaine Universitaire, B.P.72, 38402 St Martin France, jimoid@club-internet.fr
N. P. Smart
Affiliation:
Dept. Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB United Kingdom, nigel@cs.bris.ac.uk, http://www.cs.bris.ac.uk/~nigel frederik@cs.bris.ac.uk, http://www.cs.bris.ac.uk/~frederik
F. Vercauteren
Affiliation:
Dept. Computer Science, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB United Kingdom, nigel@cs.bris.ac.uk, http://www.cs.bris.ac.uk/~nigel frederik@cs.bris.ac.uk, http://www.cs.bris.ac.uk/~frederik

Abstract

In this paper, the authors re-examine the reduction of Maurer and Wolf of the discrete logarithm problem to the Diffie-Hellman problem. They give a precise estimate for the number of operations required in the reduction, and then use this to estimate the exact security of the elliptic curve variant of the Diffie-Hellman protocol for various elliptic curves defined in standards.

Type
Research Article
Copyright
Copyright © London Mathematical Society 2004

References

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