### Abstract

In the case of Barreto-Naehrig pairing-friendly curves of embedding degree 12 of order r, recent efficient Ate pairings such as R-ate, optimal, and Xate pairings achieve Miller loop lengths of . On the other hand, the twisted Ate pairing requires loop iterations, and thus is usually slower than the recent efficient Ate pairings. This paper proposes an improved twisted Ate pairing using Frobenius maps and a small scalar multiplication. The proposal splits the Miller's algorithm calculation into several independent parts, for which multi-pairing techniques apply efficiently. The maximum number of loop iterations in Miller's algorithm for the proposed twisted Ate pairing is equal to the attained by the most efficient Ate pairings.

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

Pages | 47-64 |

Number of pages | 18 |

Volume | 5984 LNCS |

DOIs | |

Publication status | Published - 2010 |

Event | 12th International Conference on Information Security and Cryptology, ICISC 2009 - Seoul, Korea, Republic of Duration: Dec 2 2009 → Dec 4 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 | 5984 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 12th International Conference on Information Security and Cryptology, ICISC 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 12/2/09 → 12/4/09 |

### Fingerprint

### Keywords

- Frobenius map
- Miller's algorithm
- multi-pairing
- thread computing
- twisted Ate pairing

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 5984 LNCS, pp. 47-64). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5984 LNCS). https://doi.org/10.1007/978-3-642-14423-3_4

**Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing.** / Sakemi, Yumi; Takeuchi, Shoichi; Nogami, Yasuyuki; Morikawa, Yoshitaka.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 5984 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5984 LNCS, pp. 47-64, 12th International Conference on Information Security and Cryptology, ICISC 2009, Seoul, Korea, Republic of, 12/2/09. https://doi.org/10.1007/978-3-642-14423-3_4

}

TY - GEN

T1 - Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing

AU - Sakemi, Yumi

AU - Takeuchi, Shoichi

AU - Nogami, Yasuyuki

AU - Morikawa, Yoshitaka

PY - 2010

Y1 - 2010

N2 - In the case of Barreto-Naehrig pairing-friendly curves of embedding degree 12 of order r, recent efficient Ate pairings such as R-ate, optimal, and Xate pairings achieve Miller loop lengths of . On the other hand, the twisted Ate pairing requires loop iterations, and thus is usually slower than the recent efficient Ate pairings. This paper proposes an improved twisted Ate pairing using Frobenius maps and a small scalar multiplication. The proposal splits the Miller's algorithm calculation into several independent parts, for which multi-pairing techniques apply efficiently. The maximum number of loop iterations in Miller's algorithm for the proposed twisted Ate pairing is equal to the attained by the most efficient Ate pairings.

AB - In the case of Barreto-Naehrig pairing-friendly curves of embedding degree 12 of order r, recent efficient Ate pairings such as R-ate, optimal, and Xate pairings achieve Miller loop lengths of . On the other hand, the twisted Ate pairing requires loop iterations, and thus is usually slower than the recent efficient Ate pairings. This paper proposes an improved twisted Ate pairing using Frobenius maps and a small scalar multiplication. The proposal splits the Miller's algorithm calculation into several independent parts, for which multi-pairing techniques apply efficiently. The maximum number of loop iterations in Miller's algorithm for the proposed twisted Ate pairing is equal to the attained by the most efficient Ate pairings.

KW - Frobenius map

KW - Miller's algorithm

KW - multi-pairing

KW - thread computing

KW - twisted Ate pairing

UR - http://www.scopus.com/inward/record.url?scp=77954576003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954576003&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14423-3_4

DO - 10.1007/978-3-642-14423-3_4

M3 - Conference contribution

AN - SCOPUS:77954576003

SN - 3642144225

SN - 9783642144226

VL - 5984 LNCS

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

SP - 47

EP - 64

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

ER -