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

Frank Lehmann; Markus Maurer; Volker Müller; Victor Shoup

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

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

Frank Lehmann, Markus Maurer, Volker Müller, Victor Shoup

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 F_p, where p is a 375-digit prime.

Original language	English (US)
Title of host publication	Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings
Editors	Leonard M. Adleman, Ming-Deh Huang
Publisher	Springer Verlag
Pages	60-70
Number of pages	11
ISBN (Print)	9783540586913
DOIs	https://doi.org/10.1007/3-540-58691-1_44
State	Published - 1994
Event	1st Algorithmic Number Thoery Symposium, ANTS-I 1994 - Ithaca, United States Duration: May 6 1994 → May 9 1994

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	877 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	1st Algorithmic Number Thoery Symposium, ANTS-I 1994
Country/Territory	United States
City	Ithaca
Period	5/6/94 → 5/9/94

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-58691-1_44

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

Counting the number of points on elliptic curves over finite fields of characteristic greater than three. / Lehmann, Frank; Maurer, Markus; Müller, Volker et al.
Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings. ed. / Leonard M. Adleman; Ming-Deh Huang. 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 proceeding › Conference 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 LM Adleman & M-D Huang (eds), Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings. 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. https://doi.org/10.1007/3-540-58691-1_44

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 Adleman LM, Huang MD, editors, Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings. Springer Verlag. 1994. p. 60-70. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-58691-1_44

Lehmann, Frank ; Maurer, Markus ; Müller, Volker et al. / 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. editor / Leonard M. Adleman ; Ming-Deh Huang. 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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Counting the number of points on elliptic curves over finite fields of characteristic greater than three

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