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International audienceCryptographic schemes using elliptic curves over finite fields requirethe computation of the cardinality of the curves. Dramaticprogress have been achieved recently in that field. The aim of thisarticle is to highlight part of these improvements and to describe anefficient implementation of them in the particular case of the field$GF(2^n)$, for $n \leq 500$

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