| アイテムタイプ |
学術雑誌論文 / Journal Article(1) |
| 公開日 |
2012-07-30 |
| タイトル |
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タイトル |
Tate and Ate pairings for y2 =x5−αx in characteristic five |
| 言語 |
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言語 |
eng |
| キーワード |
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|
主題Scheme |
Other |
|
主題 |
hyperelliptic curves |
| キーワード |
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主題Scheme |
Other |
|
主題 |
distortion map |
| キーワード |
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主題Scheme |
Other |
|
主題 |
Tate and Ate pairings |
| 資源タイプ |
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資源タイプ識別子 |
http://purl.org/coar/resource_type/c_6501 |
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資源タイプ |
journal article |
| 著者 |
Harasawa, Ryuichi
Sueyoshi, Yutaka
Kudo, Aichi
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| 抄録 |
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内容記述タイプ |
Abstract |
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内容記述 |
In this paper, we consider the Tate and Ate pairings for the genus-2 supersingular hyperelliptic curves y2=x5−αx (α=±2) defined over finite fields of characteristic five. More precisely, we construct a distortion map explicitly, and show that the map indeed gives an input for which the value of the Tate pairing is not trivial. We next describe a computation of the Tate pairing by using the proposed distortion map. We also see that this type of curve is equipped with a simple quintuple operation on the Jacobian group, which leads to an improvement for computing the Tate pairing. We further show the Ate pairing, a variant of the Tate pairing for elliptic curves, can be applied to this curve. The Ate pairing yields an algorithm which is about 50% more efficient than the Tate pairing in this case. |
| 書誌情報 |
Japan Journal of Industrial and Applied Mathematics
巻 24,
号 3,
p. 251-274,
発行日 2007-10
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| 出版者 |
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出版者 |
Springer |
| ISSN |
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収録物識別子タイプ |
ISSN |
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収録物識別子 |
09167005 |
| EISSN |
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収録物識別子タイプ |
ISSN |
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収録物識別子 |
1868937X |
| DOI |
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|
関連タイプ |
isVersionOf |
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|
識別子タイプ |
DOI |
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関連識別子 |
10.1007/BF03167539 |
| 権利 |
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|
権利情報 |
©日本応用数理学会 |
| 権利 |
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|
権利情報 |
The final publication is available at www.springerlink.com. |
| 著者版フラグ |
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出版タイプ |
AM |
|
出版タイプResource |
http://purl.org/coar/version/c_ab4af688f83e57aa |
| 引用 |
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内容記述タイプ |
Other |
|
内容記述 |
Japan Journal of Industrial and Applied Mathematics, 24(3), pp.251-274; 2007 |
JJIAM24_3_251.pdf (1.7 MB)
