Counting the Number of Points on Elliptic Curves over Finite Fields: Strategies and Performances

Reynald Lercier (1) , François Morain (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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 $GF(2^n)$, for $n \leq 500$.

Domaines: Géométrie algébrique [math.AG]

Reynald Lercier, François Morain. Counting the Number of Points on Elliptic Curves over Finite Fields: Strategies and Performances. EUROCRYPT '95, May 1995, Saint-Malo, France. ⟨10.1007/3-540-49264-X_7⟩. ⟨hal-01102046⟩