Presentation	2012-11-22 A New Explicit Relation between Trace, Definition Field, and Embedding Degree ATSUKO MIYAJI, XIAONAN SHI,
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Abstract(in English)	For pairing based cryptography we need elliptic curves defined over extension finite fields F_ with moderate embedding degrees κ. We say such elliptic curves are pairing-friendly. An elliptic curve is determined by mathematical parameters such as the j-invariant or the order #E(F_), therefore it is an open problem to give an explicit conditions between mathematical parameters and embedding degrees κ. Hirasawa, and Miyaji [2] presented a concrete condition of existence of elliptic curves with pre-determined embedding degrees. In this paper, we generalize their results and investigate a new explicit relation between elliptic-curve parameters and embedding degrees.
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Keyword(in English)	elliptic curves / embedding degree / pairing-based cryptography
Paper #	ISEC2012-69,LOIS2012-44
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Committee	LOIS
Conference Date	2012/11/14(1days)
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Registration To	Life Intelligence and Office Information Systems (LOIS)
Language	ENG
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	A New Explicit Relation between Trace, Definition Field, and Embedding Degree
Sub Title (in English)
Keyword(1)	elliptic curves
Keyword(2)	embedding degree
Keyword(3)	pairing-based cryptography
1st Author's Name	ATSUKO MIYAJI
1st Author's Affiliation	Japan Advanced Institute of Science and Technology()
2nd Author's Name	XIAONAN SHI
2nd Author's Affiliation	Japan Advanced Institute of Science and Technology
Date	2012-11-22
Paper #	ISEC2012-69,LOIS2012-44
Volume (vol)	vol.112
Number (no)	306
Page	pp.pp.-
#Pages	6
Date of Issue