Computing the eigenvalue in the schoof-elkies-atkin algorithm using abelian lifts

Authors:
P. Mihailescu;F. Morain;É. Schost
Affiliations:
Mathematisches Institut der Universität Göttingen, Germany;École polytechnique, Palaiseau, France;University of Western Ontario, London, ON, Canada
Venue:
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Year:
2007

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Abstract

The Schoof-Elkies-Atkin algorithm is the best known method for counting the number of points of an elliptic curve defined over a finite field of large characteristic. We use Abelian properties of division polynomials to design a fast theoretical and practical algorithm for nding the eigenvalue.