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

Pages | 25-39 |

Number of pages | 15 |

Publication status | Published - Dec 1 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) |
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Volume | 4547 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

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

City | Madrid |

Period | 6/21/07 → 6/22/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

_{T}pairing in characteristic three. In

*Arithmetic of Finite Fields - First International Workshop, WAIFI 2007, Proceedings*(pp. 25-39). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4547 LNCS).

**A coprocessor for the final exponentiation of the η _{T} pairing in characteristic three.** / Beuchat, Jean Luc; Brisebarre, Nicolas; Shirase, Masaaki; Takagi, Tsuyoshi; Okamoto, Eiji.

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

_{T}pairing in characteristic three. in

*Arithmetic of Finite Fields - First International Workshop, WAIFI 2007, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4547 LNCS, pp. 25-39, 1st International Workshop on Arithmetic of Finite Fields, WAIFI 2007, Madrid, Spain, 6/21/07.

_{T}pairing in characteristic three. In Arithmetic of Finite Fields - First International Workshop, WAIFI 2007, Proceedings. 2007. p. 25-39. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

}

TY - GEN

T1 - A coprocessor for the final exponentiation of the ηT pairing in characteristic three

AU - Beuchat, Jean Luc

AU - Brisebarre, Nicolas

AU - Shirase, Masaaki

AU - Takagi, Tsuyoshi

AU - Okamoto, Eiji

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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 ηT 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 ηT 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 sign397 and show that a coprocessor based on a single such operator meets this timing constraint.

AB - 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 ηT 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 ηT 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 sign397 and show that a coprocessor based on a single such operator meets this timing constraint.

UR - http://www.scopus.com/inward/record.url?scp=38149033707&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:38149033707

SN - 9783540730736

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

SP - 25

EP - 39

BT - Arithmetic of Finite Fields - First International Workshop, WAIFI 2007, Proceedings

ER -