### Abstract

In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log_{2} r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log _{2}r] to[log_{2}(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ". For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log_{2}X].

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 | 178-191 |

Number of pages | 14 |

Volume | 5209 LNCS |

DOIs | |

Publication status | Published - 2008 |

Event | 2nd International Conference on Pairing-Based Cryptography, Pairing 2008 - Egham, United Kingdom Duration: Sep 1 2008 → Sep 3 2008 |

### 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 | 5209 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 2nd International Conference on Pairing-Based Cryptography, Pairing 2008 |
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Country | United Kingdom |

City | Egham |

Period | 9/1/08 → 9/3/08 |

### Fingerprint

### Keywords

- Ate pairing
- Miller's algorithm

### 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. 5209 LNCS, pp. 178-191). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5209 LNCS). https://doi.org/10.1007/978-3-540-85538-5_13

**Integer variable x-based ate pairing.** / Nogami, Yasuyuki; Akane, Masataka; Sakemi, Yumi; Kato, Hidehiro; 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. 5209 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5209 LNCS, pp. 178-191, 2nd International Conference on Pairing-Based Cryptography, Pairing 2008, Egham, United Kingdom, 9/1/08. https://doi.org/10.1007/978-3-540-85538-5_13

}

TY - GEN

T1 - Integer variable x-based ate pairing

AU - Nogami, Yasuyuki

AU - Akane, Masataka

AU - Sakemi, Yumi

AU - Kato, Hidehiro

AU - Morikawa, Yoshitaka

PY - 2008

Y1 - 2008

N2 - In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log2 r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log 2r] to[log2(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ". For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log2X].

AB - In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller's algorithm is log2 r/Φ(k), where Φ(•) is the Euler's function. Ate pairing reduced the number of the loops of Miller's algorithm of Tate pairing from [log 2r] to[log2(t - 1)]. Recently, it is known to systematically prepare a pairing-friendly elliptic curve whose parameters are given by a polynomial of integer variable "χ". For the curve, this paper gives integer variable χ -based Ate pairing that achieves the lower bound by reducing it to [log2X].

KW - Ate pairing

KW - Miller's algorithm

UR - http://www.scopus.com/inward/record.url?scp=52449098485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52449098485&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85538-5_13

DO - 10.1007/978-3-540-85538-5_13

M3 - Conference contribution

AN - SCOPUS:52449098485

SN - 3540855033

SN - 9783540855033

VL - 5209 LNCS

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

SP - 178

EP - 191

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

ER -