Section: New Results

Galois properties of curves for ECM

Participants : Răzvan Bărbulescu, Cyril Bouvier.

In collaboration with Joppe Bos, Peter Montgomery and Thorsten Kleinjung, Răzvan Bărbulescu and Cyril Bouvier proved some divisibility properties of the group order of an elliptic curve, using the Galois structure of its division polynomial. It explains the good behaviour of some curves that have been experimentally found to factor more numbers than others, and gives a way to find new curves with this property. The corresponding article [7] was presented in ANTS-X.