## 抄録

The security of pairing-based cryptosystems depends on the difficulty of the discrete logarithm problem (DLP) over certain types of finite fields. One of the most efficient algorithms for computing a pairing is the η _{T} pairing over supersingular curves on finite fields whose characteristic is 3. Indeed many high-speed implementations of this pairing have been reported, and it is an attractive candidate for practical deployment of pairing-based cryptosystems. The embedding degree of the η _{T} pairing is 6, so we deal with the difficulty of a DLP over the finite field GF(3 ^{6n}), where the function field sieve (FFS) is known as the asymptotically fastest algorithm of solving it. Moreover, several efficient algorithms are employed for implementation of the FFS, such as the large prime variation. In this paper, we estimate the time complexity of solving the DLP for the extension degrees n=97,163, 193,239,313,353,509, when we use the improved FFS. To accomplish our aim, we present several new computable estimation formulas to compute the explicit number of special polynomials used in the improved FFS. Our estimation contributes to the evaluation for the key length of pairing-based cryptosystems using the η _{T} pairing.

本文言語 | 英語 |
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ホスト出版物のタイトル | Information Security Practice and Experience - 8th International Conference, ISPEC 2012, Proceedings |

ページ | 228-244 |

ページ数 | 17 |

DOI | |

出版ステータス | 出版済み - 2012 |

イベント | 8th International Conference on Information Security Practice and Experience, ISPEC 2012 - Hangzhou, 中国 継続期間: 4月 9 2012 → 4月 12 2012 |

### 出版物シリーズ

名前 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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巻 | 7232 LNCS |

ISSN（印刷版） | 0302-9743 |

ISSN（電子版） | 1611-3349 |

### その他

その他 | 8th International Conference on Information Security Practice and Experience, ISPEC 2012 |
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国/地域 | 中国 |

City | Hangzhou |

Period | 4/9/12 → 4/12/12 |

## !!!All Science Journal Classification (ASJC) codes

- 理論的コンピュータサイエンス
- コンピュータ サイエンス（全般）

## フィンガープリント

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