The equivalence between the DHP and DLP for elliptic curves used in practical applicationsNigel Smart, Fre Vercauteren, A. Muzereau, The equivalence between the DHP and DLP for elliptic curves used in practical applications. LMS Journal of Computation and Mathematics, 7, pp. 50–72. March 2004. No electronic version available. External information
We re-examine the reduction of Maurer and Wolf of the Discrete Logarithm problem to the Diffie--Hellman problem. We give a precise estimate for the number of operations required in the reduction and use this to estimate the exact security of the elliptic curve variant of the Diffie--Hellman protocol for various elliptic curves defined in standards.