IJPAM: Volume 42, No. 4 (2008)

CONSTRUCTING ELLIPTIC CURVES
WITH GIVEN WEIL PAIRING

Hugues Verdure
Department of Mathematics
Faculty of Education
Bergen University College
P.O. Box 7030, Bergen, 5020, NORWAY
e-mail: Hugues.Verdure@hib.no


Abstract.We give a parametrization of the set of isomorphism classes of triples $(E,P,Q)$, where $E$ is an elliptic curve and $P,Q$ are rational $l$-torsion points with given Weil pairing, when $l=5,7$. When the base field is finite, we also investigate the cardinality of this set.

Received: August 17, 2007

AMS Subject Classification: 14H52, 12E05

Key Words and Phrases: elliptic curve, Weil pairing

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 4