Date: 13 Jul 2001

Counting the number of points on elliptic curves over finite fields: strategies and performances

Abstract

Cryptographic schemes using elliptic curves over finite fields require the computation of the cardinality of the curves. Dramatic progress have been achieved recently in that field by various authors. The aim of this article is to highlight part of these improvements and to describe an efficient implementation of them in the particular case of the fields GF(2n), for n ≤ 600.
On leave from the French Department of Defense, Délégation Générale pour l’Armement.
Part of this study was done under contract no0044193 with DGA/CELAR.