### Abstract

The ηT pairing on supersingular is one of the most efficient algorithms for computing the bilinear pairing [3]. The rfr pairing defined over finite field F_{3n} has embedding degree 6, so that it is particularly efficient for higher security with large extension degree n. Note that the explicit algorithm over F_{3n} in [3] is designed just for n Ξ 1 (mod 12), and it is relatively complicated to construct an explicit algorithm for n ≢ 1 (mod 12). It is better that we can select many n's to implement the r¡T pairing, since n corresponds to security level of the ηT pairing. In this paper we construct an explicit algorithm for computing the ηT pairing with arbitrary extension degree n. However, the algorithm should contain many branch conditions depending on n and the curve parameters, that is undesirable for implementers of the ηT pairing. This paper then proposes the universal ηT pairing (ηT pairing), which satisfies the bilinearity of pairing (compatible with Tate pairing) without any branches in the program, and is as efficient as the original one. Therefore the proposed universal ηT pairing is suitable for the implementation of various extension degrees n with higher security.

Original language | English |
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Title of host publication | Information Security Applications - 8th International Workshop, WISA 2007, Revised Selected Papers |

Pages | 1-15 |

Number of pages | 15 |

Publication status | Published - Dec 1 2007 |

Event | 8th International Workshop on Information Security Applications, WISA 2007 - Jeju Island, Korea, Republic of Duration: Aug 27 2007 → Aug 29 2007 |

### 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 | 4867 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 8th International Workshop on Information Security Applications, WISA 2007 |
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Country | Korea, Republic of |

City | Jeju Island |

Period | 8/27/07 → 8/29/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Information Security Applications - 8th International Workshop, WISA 2007, Revised Selected Papers*(pp. 1-15). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4867 LNCS).

**Universal ηT pairing algorithm over arbitrary extension degree.** / Shirase, Masaaki; Kawahara, Yuto; Takagi, Tsuyoshi; Okamoto, Eiji.

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

*Information Security Applications - 8th International Workshop, WISA 2007, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4867 LNCS, pp. 1-15, 8th International Workshop on Information Security Applications, WISA 2007, Jeju Island, Korea, Republic of, 8/27/07.

}

TY - GEN

T1 - Universal ηT pairing algorithm over arbitrary extension degree

AU - Shirase, Masaaki

AU - Kawahara, Yuto

AU - Takagi, Tsuyoshi

AU - Okamoto, Eiji

PY - 2007/12/1

Y1 - 2007/12/1

N2 - The ηT pairing on supersingular is one of the most efficient algorithms for computing the bilinear pairing [3]. The rfr pairing defined over finite field F3n has embedding degree 6, so that it is particularly efficient for higher security with large extension degree n. Note that the explicit algorithm over F3n in [3] is designed just for n Ξ 1 (mod 12), and it is relatively complicated to construct an explicit algorithm for n ≢ 1 (mod 12). It is better that we can select many n's to implement the r¡T pairing, since n corresponds to security level of the ηT pairing. In this paper we construct an explicit algorithm for computing the ηT pairing with arbitrary extension degree n. However, the algorithm should contain many branch conditions depending on n and the curve parameters, that is undesirable for implementers of the ηT pairing. This paper then proposes the universal ηT pairing (ηT pairing), which satisfies the bilinearity of pairing (compatible with Tate pairing) without any branches in the program, and is as efficient as the original one. Therefore the proposed universal ηT pairing is suitable for the implementation of various extension degrees n with higher security.

AB - The ηT pairing on supersingular is one of the most efficient algorithms for computing the bilinear pairing [3]. The rfr pairing defined over finite field F3n has embedding degree 6, so that it is particularly efficient for higher security with large extension degree n. Note that the explicit algorithm over F3n in [3] is designed just for n Ξ 1 (mod 12), and it is relatively complicated to construct an explicit algorithm for n ≢ 1 (mod 12). It is better that we can select many n's to implement the r¡T pairing, since n corresponds to security level of the ηT pairing. In this paper we construct an explicit algorithm for computing the ηT pairing with arbitrary extension degree n. However, the algorithm should contain many branch conditions depending on n and the curve parameters, that is undesirable for implementers of the ηT pairing. This paper then proposes the universal ηT pairing (ηT pairing), which satisfies the bilinearity of pairing (compatible with Tate pairing) without any branches in the program, and is as efficient as the original one. Therefore the proposed universal ηT pairing is suitable for the implementation of various extension degrees n with higher security.

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UR - http://www.scopus.com/inward/citedby.url?scp=38549139643&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:38549139643

SN - 354077534X

SN - 9783540775348

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

SP - 1

EP - 15

BT - Information Security Applications - 8th International Workshop, WISA 2007, Revised Selected Papers

ER -