### Abstract

Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we discuss several algorithms to compute the η^{T} pairing in characteristic three and suggest further improvements. These algorithms involve addition, multiplication, cubing, inversion, and sometimes cube root extraction over F_{3}m. We propose a hardware accelerator based on a unified arithmetic operator able to perform the operations required by a given algorithm. We describe the implementation of a compact coprocessor for the field F_{3}97) given by F_{3}[x]/(x^{97} + x^{12} + 2), which compares favorably with other solutions described in the open literature.

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

Pages (from-to) | 1454-1468 |

Number of pages | 15 |

Journal | IEEE Transactions on Computers |

Volume | 57 |

Issue number | 11 |

DOIs | |

Publication status | Published - Oct 22 2008 |

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### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics

### Cite this

_{T}pairing in characteristic three.

*IEEE Transactions on Computers*,

*57*(11), 1454-1468. https://doi.org/10.1109/TC.2008.103

**Algorithms and arithmetic operators for computing the η _{T} pairing in characteristic three.** / Beuchat, Jean Luc; Brisebarre, Nicolas; Detrey, Jérémie; Okamoto, Eiji; Shirase, Masaaki; Takagi, Tsuyoshi.

Research output: Contribution to journal › Article

_{T}pairing in characteristic three',

*IEEE Transactions on Computers*, vol. 57, no. 11, pp. 1454-1468. https://doi.org/10.1109/TC.2008.103

_{T}pairing in characteristic three. IEEE Transactions on Computers. 2008 Oct 22;57(11):1454-1468. https://doi.org/10.1109/TC.2008.103

}

TY - JOUR

T1 - Algorithms and arithmetic operators for computing the ηT pairing in characteristic three

AU - Beuchat, Jean Luc

AU - Brisebarre, Nicolas

AU - Detrey, Jérémie

AU - Okamoto, Eiji

AU - Shirase, Masaaki

AU - Takagi, Tsuyoshi

PY - 2008/10/22

Y1 - 2008/10/22

N2 - Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we discuss several algorithms to compute the ηT pairing in characteristic three and suggest further improvements. These algorithms involve addition, multiplication, cubing, inversion, and sometimes cube root extraction over F3m. We propose a hardware accelerator based on a unified arithmetic operator able to perform the operations required by a given algorithm. We describe the implementation of a compact coprocessor for the field F397) given by F3[x]/(x97 + x12 + 2), which compares favorably with other solutions described in the open literature.

AB - Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we discuss several algorithms to compute the ηT pairing in characteristic three and suggest further improvements. These algorithms involve addition, multiplication, cubing, inversion, and sometimes cube root extraction over F3m. We propose a hardware accelerator based on a unified arithmetic operator able to perform the operations required by a given algorithm. We describe the implementation of a compact coprocessor for the field F397) given by F3[x]/(x97 + x12 + 2), which compares favorably with other solutions described in the open literature.

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UR - http://www.scopus.com/inward/citedby.url?scp=54049118059&partnerID=8YFLogxK

U2 - 10.1109/TC.2008.103

DO - 10.1109/TC.2008.103

M3 - Article

AN - SCOPUS:54049118059

VL - 57

SP - 1454

EP - 1468

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

SN - 0018-9340

IS - 11

ER -