Counting the number of points on elliptic curves over finite fields of characteristic greater than three

  • Frank Lehmann
  • Markus Maurer
  • Volker Müller
  • Victor Shoup
Conference paper

DOI: 10.1007/3-540-58691-1_44

Part of the Lecture Notes in Computer Science book series (LNCS, volume 877)
Cite this paper as:
Lehmann F., Maurer M., Müller V., Shoup V. (1994) Counting the number of points on elliptic curves over finite fields of characteristic greater than three. In: Adleman L.M., Huang MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg

Abstract

We present a variant of an algorithm of Oliver Atkin for counting the number of points on an elliptic curve over a finite field. We describe an implementation of this algorithm for prime fields. We report on the use of this implementation to count the number of points on a curve over \(\mathbb{F}\)p, where p is a 375-digit prime.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Frank Lehmann
    • 1
  • Markus Maurer
    • 1
  • Volker Müller
    • 1
  • Victor Shoup
    • 1
  1. 1.FB InformatikUniversität des SaarlandesSaarbrückenGermany

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