Paper Abstract and Keywords |
Presentation |
2009-03-10 09:25
Elliptic curves with a pre-determined embedding degree Shoujirou Hirasawa, Atsuko Miyaji (JAIST) IT2008-79 ISEC2008-137 WBS2008-92 |
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 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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IT2008-79 ISEC2008-137 WBS2008-92 |
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) |
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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) |
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embedding degree |
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pairing |
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elliptic curve |
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DLP |
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ECDLP |
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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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Speaker |
Author-1 |
Date Time |
2009-03-10 09:25:00 |
Presentation Time |
25 minutes |
Registration for |
ISEC |
Paper # |
IT2008-79, ISEC2008-137, WBS2008-92 |
Volume (vol) |
vol.108 |
Number (no) |
no.472(IT), no.473(ISEC), no.474(WBS) |
Page |
pp.223-229 |
#Pages |
7 |
Date of Issue |
2009-03-02 (IT, ISEC, WBS) |
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