Counting the number of points on elliptic curves over finite fields: strategies and performances

  • Reynald Lercier
  • François Morain
Conference paper

DOI: 10.1007/3-540-49264-X_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 921)
Cite this paper as:
Lercier R., Morain F. (1995) Counting the number of points on elliptic curves over finite fields: strategies and performances. In: Guillou L.C., Quisquater JJ. (eds) Advances in Cryptology — EUROCRYPT ’95. EUROCRYPT 1995. Lecture Notes in Computer Science, vol 921. Springer, Berlin, Heidelberg

Abstract

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 by various authors. 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 fields GF(2n), for n ≤ 600.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Reynald Lercier
    • 1
  • François Morain
    • 2
  1. 1.CELAR/SSIGBruz
  2. 2.École PolytechniqueLIXPalaiseau CedexFrance

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