## Abstract

Since the introduction of pairings over (hyper)elliptic curves in constructive cryptographic applications, an ever increasing number of protocols based on pairings have appeared in the literature. Software implementations being rather slow, the study of hardware architectures became an active research area. Beuchat et al. proposed for instance a coprocessor which computes the characteristic three η_{T} pairing, from which the Tate pairing can easily be derived, in 33μs on a Cyclone II FPGA. However, a final exponentiation is required to ensure a unique output value and the authors proposed to supplement their η_{T} pairing accelerator with a coprocessor for exponentiation. Thus, the challenge consists in designing the smallest possible piece of hardware able to perform this task in less than 33 /is on a Cyclone II device. In this paper, we propose a novel arithmetic operator implementing addition, cubing, and multiplication over double-struck F sign_{397} and show that a coprocessor based on a single such operator meets this timing constraint.

Original language | English |
---|---|

Title of host publication | Arithmetic of Finite Fields - First International Workshop, WAIFI 2007, Proceedings |

Publisher | Springer Verlag |

Pages | 25-39 |

Number of pages | 15 |

ISBN (Print) | 9783540730736 |

DOIs | |

Publication status | Published - 2007 |

Event | 1st International Workshop on Arithmetic of Finite Fields, WAIFI 2007 - Madrid, Spain Duration: Jun 21 2007 → Jun 22 2007 |

### Publication series

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

Volume | 4547 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st International Workshop on Arithmetic of Finite Fields, WAIFI 2007 |
---|---|

Country/Territory | Spain |

City | Madrid |

Period | 6/21/07 → 6/22/07 |

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint

Dive into the research topics of 'A coprocessor for the final exponentiation of the η_{T}pairing in characteristic three'. Together they form a unique fingerprint.