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Medientyp:
E-Artikel
Titel:
Counting points on elliptic curves over finite fields
Beteiligte:
SCHOOF, René
Erschienen:
Institut de mathématiques de Bordeaux, 1995
Erschienen in:Journal de Théorie des Nombres de Bordeaux
Sprache:
Englisch
ISSN:
1246-7405;
2118-8572
Entstehung:
Anmerkungen:
Beschreibung:
<p>We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic polynomial time algorithm was impractical in its original form. We discuss several practical improvements by Atkin and Elkies.</p>