### Abstract

We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8% to 8.5% over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P+Q from given points P, Q on the curve. We give applications to simultaneous multiple scalar multiplication and to the Elliptic Curve Method of factorization. We show how this improvement together with another idea can speed the computation of the Weil and Tate pairings by up to 7.8%.

Original language | English (US) |
---|---|

Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Marc Joye |

Publisher | Springer Verlag |

Pages | 343-354 |

Number of pages | 12 |

ISBN (Print) | 3540008470, 9783540008477 |

DOIs | |

State | Published - 2003 |

### Publication series

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

Volume | 2612 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Fast elliptic curve arithmetic and improved weil pairing evaluation'. Together they form a unique fingerprint.

## Cite this

Eisenträger, K., Lauter, K., & Montgomery, P. L. (2003). Fast elliptic curve arithmetic and improved weil pairing evaluation. In M. Joye (Ed.),

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 343-354). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2612). Springer Verlag. https://doi.org/10.1007/3-540-36563-x_24