Counting the Number of Points on Elliptic Curves over Finite Fields: Strategies and Performances
Résumé
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. 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 field
$GF(2^n)$, for $n \leq 500$.