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Paper Abstract and Keywords
Presentation 2009-03-10 09:25
Elliptic curves with a pre-determined embedding degree
Shoujirou Hirasawa, Atsuko Miyaji (JAIST)
Abstract (in Japanese) (See Japanese page) 
(in English) A paring over an elliptic-curve E(F_{p^m}) to an extension field of F_{p^{mk}} has begun to be attractive to cryptosystems, where k is called the embedding degree. The cryptosystems using a paring are called the paring-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_{p^m}) is reduced to DLP over F_{p^{mk}}. The elliptic-curve is determined by j-invariant or order, but the relationship between these parameters and the embedding degree has not been described explicitly without a special case. In this paper, we improve the method to construct elliptic-curves with pre-determind embedding degrees, and present some examples of the elliptic-curves over 160-bit, 192-bit and 224-bit F_{p^m}.
Keyword (in Japanese) (See Japanese page) 
(in English) embedding degree / pairing / elliptic curve / DLP / ECDLP / / /  
Reference Info. IEICE Tech. Rep., vol. 108, no. 473, ISEC2008-137, pp. 223-229, March 2009.
Paper # ISEC2008-137 
Date of Issue 2009-03-02 (IT, ISEC, WBS) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380

Conference Information
Committee WBS IT ISEC  
Conference Date 2009-03-09 - 2009-03-10 
Place (in Japanese) (See Japanese page) 
Place (in English) Hakodate Mirai Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To ISEC 
Conference Code 2009-03-WBS-IT-ISEC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Elliptic curves with a pre-determined embedding degree 
Sub Title (in English)  
Keyword(1) embedding degree  
Keyword(2) pairing  
Keyword(3) elliptic curve  
Keyword(4) DLP  
Keyword(5) ECDLP  
1st Author's Name Shoujirou Hirasawa  
1st Author's Affiliation Japan Advanced Institute of Science and Technology (JAIST)
2nd Author's Name Atsuko Miyaji  
2nd Author's Affiliation Japan Advanced Institute of Science and Technology (JAIST)
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Date Time 2009-03-10 09:25:00 
Presentation Time 25 
Registration for ISEC 
Paper # IEICE-IT2008-79,IEICE-ISEC2008-137,IEICE-WBS2008-92 
Volume (vol) IEICE-108 
Number (no) no.472(IT), no.473(ISEC), no.474(WBS) 
Page pp.223-229 
#Pages IEICE-7 
Date of Issue IEICE-IT-2009-03-02,IEICE-ISEC-2009-03-02,IEICE-WBS-2009-03-02 

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