2015 Fiscal Year Final Research Report
Study of construction of pairing-friendly elliptic curves and hyper elliptic curves
| Project/Area Number |
26870486
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Information security
Algebra
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| Research Institution | Tsuru University |
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Principal Investigator |
Okano Keiji 都留文科大学, 文学部, 講師 (70454022)
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| Project Period (FY) |
2014-04-01 – 2016-03-31
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| Keywords | ペアリングを用いた公開鍵暗号系 / 楕円曲線 / 埋め込み次数 |
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| Outline of Final Research Achievements |
Pairing-based cryptographic schemes require elliptic or hyperelliptic curves with special properties. In this research, we study the condition that complete families of such curves are ideal, and we give the followings:
(1) There are no ideal complete families of pairing-friendly elliptic curves with embedding degree 3, 4, or 6.
(2) Many complete families, including non-cyclotomic case, of pairing-friendly elliptic curves the embedding degree 8 or 12 are non-ideal.
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| Free Research Field |
代数学
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