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b10-1. 雑誌掲載論文 >
このアイテムの引用には次の識別子を使用してください:
http://hdl.handle.net/10119/10046
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| タイトル: | New Concrete Relation between Trace, Definition Field, and Embedding Degree |
| 著者: | Hirasawa, Shoujirou
Miyaji, Atsuko |
| キーワード: | elliptic curve
embedding degree |
| 発行日: | 2011-06-01 |
| 出版者: | 電子情報通信学会 |
| 誌名: | IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences |
| 巻: | E94-A |
| 号: | 6 |
| 開始ページ: | 1368 |
| 終了ページ: | 1374 |
| 抄録: | A pairing over an elliptic curve E/F_<pm> to an extension field of Fp_<mk> has begun to be attractive in cryptosystems, from the practical and theoretical point of view. From the practical point of view, many cryptosystems using a pairing, called the pairing-based cryptosystems, have been proposed and, thus, a pairing is a necessary tool for cryptosystems. From the theoretical point of view, the so-called embedding degree k is an indicator of a relationship between the elliptic curve Discrete Logarithm Problem (ECDLP) and the Discrete Logarithm Problem (DLP), where ECDLP over E(F_<pm>) is reduced to DLP over Fp_<mk> by using the pairing. An elliptic curve is determined by mathematical parameters such as the j-invariant or order of an elliptic curve, however, explicit conditions between these mathematical parameters and an embedding degree have been described only in a few degrees. In this paper, we focus on the theoretical view of a pairing and investigate a new condition of the existence of elliptic curves with pre-determined embedding degrees. We also present some examples of elliptic curves over 160-bit, 192-bit and 224-bit F_<pm> with embedding degrees k < (log p)^2 such as k=10, 12, 14, 20, 22, 24, 28. |
| Rights: | Copyright (C)2011 IEICE. Shoujirou Hirasawa and Atsuko Miyaji, IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences, E94-A(6), 2011, 1368-1374. http://www.ieice.org/jpn/trans_online/ |
| URI: | http://hdl.handle.net/10119/10046 |
| 資料タイプ: | publisher |
| 出現コレクション: | b10-1. 雑誌掲載論文 (Journal Articles)
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このアイテムのファイル:
| ファイル |
記述 |
サイズ | 形式 |
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| 16544-1.pdf | | 238Kb | Adobe PDF | 見る/開く |
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