We estimate the
probabilities that the Menezes-Okamoto-Vanstone
reduction of the discrete logarithm problem
on an elliptic curve $\E$ to the discrete logarithm problem
in a certain finite field succeeds for various groups
on points on $\E$. Our bounds imply that in all interesting
cases these probabilities are exponentially small.
This extends results of Balasubramanian
and Koblitz who have treated the instance in which the order
of the group of points on $\E$ is prime.
Publié le : 2004-07-15
Classification:
11G20,
11T71,
14G15,
14G50
@article{1258131069,
author = {Luca, Florian and Mireles, David Jose and Shparlinski, Igor E.},
title = {MOV attack in various subgroups on elliptic curves},
journal = {Illinois J. Math.},
volume = {48},
number = {3},
year = {2004},
pages = { 1041-1052},
language = {en},
url = {http://dml.mathdoc.fr/item/1258131069}
}
Luca, Florian; Mireles, David Jose; Shparlinski, Igor E. MOV attack in various subgroups on elliptic curves. Illinois J. Math., Tome 48 (2004) no. 3, pp. 1041-1052. http://gdmltest.u-ga.fr/item/1258131069/