  We indicate a strategy in order to construct bilinear multiplication
algorithms of type Chudnovsky in large extensions of any finite field. In
particular, by using the symmetric version of the generalization of
Randriambololona specialized on the elliptic curves, we show that it is
possible to construct such algorithms with low bilinear complexity. More
precisely, if we only consider the Chudnovsky-type algorithms of type symmetric
elliptic, we show that the symmetric bilinear complexity of these algorithms is
in $O(n(2q)^{\log_q^*(n)})$ where $n$ corresponds to the extension degree, and
$\log_q^*(n)$ is the iterated logarithm. Moreover, we show that the
construction of such algorithms can be done in time polynomial in $n$. Finally,
applying this method we present the effective construction, step by step, of
such an algorithm of multiplication in the finite field $\F_{3^{57}}$.
