The Equivalence between the DHP and DLP for Elliptic Curves Used in Practical Applications
A. Muzereau, N. P. Smart, Fréderik Vercauteren · LMS Journal of Computation and Mathematics · 2004
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.