Paper Abstract and Keywords |
Presentation |
2014-11-21 14:40
Elliptic curves subjected to the GHS attack over prime degree extension fields in odd characteristic Tsutomu Iijima (Koden), Jinhui Chao (Chuo Univ) ISEC2014-59 SITE2014-50 LOIS2014-29 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
One of the most powerful attacks to elliptic curve and hyperelliptic based cryptosystems defined over an extension of a finite field is known as the GHS attack or cover attack.
This attack maps the discrete logarithm problem (DLP) in the Jacobian of a curve $C_{0}$ defined over the $d$ degree extension field $k_{d}$ of $k:=mathbb{F}_{q}$ to the DLP in the Jacobian of a covering curve $C$ of $C_{0}$ over $k$.
However, understanding including analysis of and defence against this attack has been a rather nontrivial task. Recently, a complete classification for elliptic curves $C_{0}$ over prime degree extension fields of odd characteristic which possess $(2,...,2)$ covering $C/k$ of $mathbb{P}^{1}$, or a complete list of all elliptic curves subjected to this attack was obtained.
In this paper, we first explain implication and usage of this result of classification or the list.
Next, based on this classification list, we discuss elliptic curves $C_{0}/k_{d}$ subjected to the GHS attack and certain class of secure elliptic curves against the GHS attack. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Elliptic/Hyperelliptic curves / Elliptic/Hyperelliptic curve cryptosystems / GHS attack / Covering curves / Galois representation / / / |
Reference Info. |
IEICE Tech. Rep., vol. 114, no. 319, ISEC2014-59, pp. 19-26, Nov. 2014. |
Paper # |
ISEC2014-59 |
Date of Issue |
2014-11-14 (ISEC, SITE, LOIS) |
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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ISEC2014-59 SITE2014-50 LOIS2014-29 |
Conference Information |
Committee |
ISEC LOIS SITE |
Conference Date |
2014-11-21 - 2014-11-22 |
Place (in Japanese) |
(See Japanese page) |
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Paper Information |
Registration To |
ISEC |
Conference Code |
2014-11-ISEC-LOIS-SITE |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Elliptic curves subjected to the GHS attack over prime degree extension fields in odd characteristic |
Sub Title (in English) |
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Keyword(1) |
Elliptic/Hyperelliptic curves |
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Elliptic/Hyperelliptic curve cryptosystems |
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GHS attack |
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Covering curves |
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Galois representation |
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1st Author's Name |
Tsutomu Iijima |
1st Author's Affiliation |
Koden Electronics Co.,Ltd. (Koden) |
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Jinhui Chao |
2nd Author's Affiliation |
Chuo University (Chuo Univ) |
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Speaker |
Author-1 |
Date Time |
2014-11-21 14:40:00 |
Presentation Time |
25 minutes |
Registration for |
ISEC |
Paper # |
ISEC2014-59, SITE2014-50, LOIS2014-29 |
Volume (vol) |
vol.114 |
Number (no) |
no.319(ISEC), no.320(SITE), no.321(LOIS) |
Page |
pp.19-26 |
#Pages |
8 |
Date of Issue |
2014-11-14 (ISEC, SITE, LOIS) |
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