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International audienceOne of the main difficulties for implementing cryptographic schemes  based on elliptic curves defined over finite fields is the necessary  computation of the cardinality of these curves. In the case of  finite fields $GF(2^n)$, recent theoretical breakthroughs yield a  significant speed up of the computations. Once described some of  these ideas in the first part of this paper, we show that our  current implementation runs from 2 up to 10 times faster than what  was done previously. In the second part, we exhibit a slight change  of Schoof's algorithm to choose curves with a number of points  ``nearly'' prime and so construct cryptosystems based on random  elliptic curves instead of specific curves as it used to be

Finding Good Random Elliptic Curves for Cryptosystems Defined over $$ \mathbb{F}_{{\text{2}}^n } $$