Abstract
In this Note, we improve a result of Shokrollahi who has applied the algorithm of D.V. Chudnovsky and G.V. Chudnovsky to algebraic curves of genus one. More precisely, from the Abelian group structure of the set of rational points on elliptic curves, we show that, if 1 2 q + 1 < n ⩽ 1 2 ( q + 1 + ϵ ( q ) ) , then the bilinear complexity of the multiplication in all extensions F q n is equal to 2 n. To cite this article: J. Chaumine, C. R. Acad. Sci. Paris, Ser. I 343 (2006).
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