### 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) |
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Title of host publication | Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings |

Publisher | Springer Verlag |

Pages | 60-70 |

Number of pages | 11 |

Volume | 877 LNCS |

ISBN (Print) | 9783540586913 |

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) |
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Volume | 877 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st Algorithmic Number Thoery Symposium, ANTS-I 1994 |
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Country | United States |

City | Ithaca |

Period | 5/6/94 → 5/9/94 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Counting the number of points on elliptic curves over finite fields of characteristic greater than three

AU - Lehmann, Frank

AU - Maurer, Markus

AU - Müller, Volker

AU - Shoup, Victor

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85028846036&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028846036&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85028846036

SN - 9783540586913

VL - 877 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 60

EP - 70

BT - Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings

PB - Springer Verlag

ER -