### 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