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

Frank Lehmann, Markus Maurer, Volker Müller, Victor Shoup

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 Fp, where p is a 375-digit prime.

Original languageEnglish (US)
Title of host publicationAlgorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings
EditorsLeonard M. Adleman, Ming-Deh Huang
PublisherSpringer Verlag
Pages60-70
Number of pages11
ISBN (Print)9783540586913
DOIs
StatePublished - 1994
Event1st Algorithmic Number Thoery Symposium, ANTS-I 1994 - Ithaca, United States
Duration: May 6 1994May 9 1994

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume877 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st Algorithmic Number Thoery Symposium, ANTS-I 1994
CountryUnited States
CityIthaca
Period5/6/945/9/94

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    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 L. M. Adleman, & M-D. Huang (Eds.), Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings (pp. 60-70). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 877 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-58691-1_44