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
PublisherSpringer Verlag
Pages60-70
Number of pages11
Volume877 LNCS
ISBN (Print)9783540586913
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

Fingerprint

Elliptic Curves
Galois field
Counting
Digit
Count
Curve

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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 Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings (Vol. 877 LNCS, 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.

Counting the number of points on elliptic curves over finite fields of characteristic greater than three. / Lehmann, Frank; Maurer, Markus; Müller, Volker; Shoup, Victor.

Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings. Vol. 877 LNCS Springer Verlag, 1994. p. 60-70 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 877 LNCS).

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

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 Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings. vol. 877 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 877 LNCS, Springer Verlag, pp. 60-70, 1st Algorithmic Number Thoery Symposium, ANTS-I 1994, Ithaca, United States, 5/6/94.
Lehmann F, Maurer M, Müller V, Shoup V. Counting the number of points on elliptic curves over finite fields of characteristic greater than three. In Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings. Vol. 877 LNCS. Springer Verlag. 1994. p. 60-70. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Lehmann, Frank ; Maurer, Markus ; Müller, Volker ; Shoup, Victor. / Counting the number of points on elliptic curves over finite fields of characteristic greater than three. Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings. Vol. 877 LNCS Springer Verlag, 1994. pp. 60-70 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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