Abstract
We estimate the probabilities that the Menezes-Okamoto-Vanstone reduction of the discrete logarithm problem on an elliptic curve double struck E sign to the discrete logarithm problem in a certain finite field succeeds for various groups on points on double struck E sign. 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 double struck E sign is prime.
| Original language | English |
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| Pages (from-to) | 1041-1052 |
| Number of pages | 12 |
| Journal | Illinois Journal of Mathematics |
| Volume | 48 |
| Issue number | 3 |
| Publication status | Published - Sept 2004 |