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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/10119/9095
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| タイトル: | Elliptic curves with a pre-determined embedding degree |
| 著者: | Hirasawa, Shoujirou
Miyaji, Atsuko |
| キーワード: | Elliptic Curves |
| 発行日: | 2009 |
| 出版者: | Institute of Electrical and Electronics Engineers (IEEE) |
| 誌名: | IEEE International Symposium on Information Theory, 2009. ISIT 2009. |
| 開始ページ: | 2391 |
| 終了ページ: | 2395 |
| DOI: | 10.1109/ISIT.2009.5206002 |
| 抄録: | A pairing over an elliptic curve E(F_<pm>) to an extension field of F_<pmk> has begun to be attractive in cryptosystems, where k is called the embedding degree. The cryptosystems using a pairing are called the pairing-based cryptosystems. The embedding degree k is also an indicator of the 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 F_<pmk>. An elliptic curve is determined by j-invarient or order, however the explicit condition between these parameters and an embedding degree has been described only in some degrees. In this paper, we investigate a new condition of the existence of elliptic curves with pre-determined embedding degrees, and present some examples of the elliptic curves over 160-bit, 192-bit and 224-bit F_<pm>. |
| Rights: | Copyright (C) 2009 IEEE. Reprinted from IEEE International Symposium on Information Theory, 2009. ISIT 2009., 2009, 2391-2395. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of JAIST's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. |
| URI: | http://hdl.handle.net/10119/9095 |
| 資料タイプ: | publisher |
| 出現コレクション: | b11-1. 会議発表論文・発表資料 (Conference Papers)
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| 13747-1.pdf | | 729Kb | Adobe PDF | 見る/開く |
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