### Abstract

When we implement the η _{T} pairing, which is one of the fastest pairings, we need multiplications in a base field and in a group G. We have previously regarded elements in G as those in to implement the η _{T} pairing. Gorla et al. proposed a multiplication algorithm in that takes 5 multiplications in , namely 15 multiplications in . This algorithm then reaches the theoretical lower bound of the number of multiplications. On the other hand, we may also regard elements in G as those in the residue group in which βa is equivalent to a for and . This paper proposes an algorithm for computing a multiplication in the residue group. Its cost is asymptotically 12 multiplications in as m → ∞, which reaches beyond the lower bound the algorithm of Gorla et al. reaches. The proposed algorithm is especially effective when multiplication in the finite field is implemented using a basic method such as shift-and-add.

Original language | English |
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Title of host publication | Selected Areas in Cryptography - 16th Annual International Workshop, SAC 2009, Revised Selected Papers |

Pages | 364-375 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Dec 1 2009 |

Event | 16th Annual International Workshop on Selected Areas in Cryptography, SAC 2009 - Calgary, AB, Canada Duration: Aug 13 2009 → Aug 14 2009 |

### 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 | 5867 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th Annual International Workshop on Selected Areas in Cryptography, SAC 2009 |
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Country | Canada |

City | Calgary, AB |

Period | 8/13/09 → 8/14/09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

_{T}pairing over. In

*Selected Areas in Cryptography - 16th Annual International Workshop, SAC 2009, Revised Selected Papers*(pp. 364-375). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5867 LNCS). https://doi.org/10.1007/978-3-642-05445-7_23