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.
|Translated title of the contribution||The equivalence between the DHP and DLP for elliptic curves used in practical applications|
|Pages (from-to)||50 - 72|
|Number of pages||22|
|Journal||LMS Journal of Computation and Mathematics|
|Publication status||Published - Mar 2004|
Smart, NP., Vercauteren, F., & Muzereau, A. (2004). The equivalence between the DHP and DLP for elliptic curves used in practical applications. LMS Journal of Computation and Mathematics, 7, 50 - 72. http://www.cs.bris.ac.uk/Publications/pub_info.jsp?id=2000075