Presentation	2015-03-04 A New Explicit Relation Between Trace, Definition Field, and Embedding Degree Atsuko MIYAJI, Satoru TANAKA,
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Abstract(in English)	For pairing based cryptography, elliptic curves defined over a finite fields F_ with moderate-embedding degrees k are required, where an embedding degree k for an elliptic curve is a cryptographic parameter. Such elliptic curves are said to be pairing-friendly. An elliptic curve is determined by mathematical parameters such as the j-invariant or order #E(F_). Therefore it is an open problem to determine the explicit relations between the mathematical parameters and the embedding degrees k. Hirasawa and Miyaji presented concrete relations between the mathematical parameters and the embedding degrees. In this research, a new explicit relation between elliptic-curve parameters and embedding degrees is investigated by generalizing their research.
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Keyword(in English)	elliptic curve / embedding degree / trace
Paper #	ICSS2014-76
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Conference Information
Committee	ICSS
Conference Date	2015/2/24(1days)
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Paper Information
Registration To	Information and Communication System Security (ICSS)
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 curve
Keyword(2)	embedding degree
Keyword(3)	trace
1st Author's Name	Atsuko MIYAJI
1st Author's Affiliation	School of Information Science, Japan Advanced Institute of Science and Technology()
2nd Author's Name	Satoru TANAKA
2nd Author's Affiliation	School of Information Science, Japan Advanced Institute of Science and Technology
Date	2015-03-04
Paper #	ICSS2014-76
Volume (vol)	vol.114
Number (no)	489
Page	pp.pp.-
#Pages	6
Date of Issue