Reynald Lercier

R. Lercier and F. Morain. Counting the Number of Points on Elliptic Curves over Finite Fields: Strategies and Performances. In L.C. Guillou and J.-J. Quisquater, editors, Advances in Cryptology - EUROCRYPT '95: International Conference on the Theory and Application of Cryptographic Techniques, Saint-Malo, France, May 1995. Proceedings, volume 921 of Lecture Notes in Computer Science, pages 79-94. Springer Berlin / Heidelberg, May 1995.

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(2ⁿ), for n <=500.

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