### 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 | |

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 | United States |

City | Ithaca |

Period | 5/6/94 → 5/9/94 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Counting the number of points on elliptic curves over finite fields of characteristic greater than three'. Together they form a unique fingerprint.

## 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