Presentation | 2012-11-22 A New Explicit Relation between Trace, Definition Field, and Embedding Degree ATSUKO MIYAJI, XIAONAN SHI, |
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Abstract(in Japanese) | (See Japanese page) |
Abstract(in English) | For pairing based cryptography we need elliptic curves defined over extension finite fields F_ with moderate embedding degrees κ. We say such elliptic curves are pairing-friendly. An elliptic curve is determined by mathematical parameters such as the j-invariant or the order #E(F_ ), therefore it is an open problem to give an explicit conditions between mathematical parameters and embedding degrees κ. Hirasawa, and Miyaji [2] presented a concrete condition of existence of elliptic curves with pre-determined embedding degrees. In this paper, we generalize their results and investigate a new explicit relation between elliptic-curve parameters and embedding degrees. |
Keyword(in Japanese) | (See Japanese page) |
Keyword(in English) | elliptic curves / embedding degree / pairing-based cryptography |
Paper # | ISEC2012-69,LOIS2012-44 |
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Committee | ISEC |
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Conference Date | 2012/11/14(1days) |
Place (in Japanese) | (See Japanese page) |
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Registration To | Information Security (ISEC) |
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Language | ENG |
Title (in Japanese) | (See Japanese page) |
Sub Title (in Japanese) | (See Japanese page) |
Title (in English) | A New Explicit Relation between Trace, Definition Field, and Embedding Degree |
Sub Title (in English) | |
Keyword(1) | elliptic curves |
Keyword(2) | embedding degree |
Keyword(3) | pairing-based cryptography |
1st Author's Name | ATSUKO MIYAJI |
1st Author's Affiliation | Japan Advanced Institute of Science and Technology() |
2nd Author's Name | XIAONAN SHI |
2nd Author's Affiliation | Japan Advanced Institute of Science and Technology |
Date | 2012-11-22 |
Paper # | ISEC2012-69,LOIS2012-44 |
Volume (vol) | vol.112 |
Number (no) | 305 |
Page | pp.pp.- |
#Pages | 6 |
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