Paper Abstract and Keywords |
Presentation |
2011-03-04 09:00
Construction of non-hyperelliptic coverings for elliptic curves on extension fields Hiroyuki Hara (Chuo Univ.), Tsutomu Iijima, Mahoro Shimura (Tokai Univ.), Jinhui Chao (Chuo Univ.) IT2010-92 ISEC2010-96 WBS2010-71 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
The GHS attack transfers the discrete logarithm problem(DLP) in the group of rational points of an elliptic curve over an extension of a finite field $k$, when it has a covering curve over $k$, into the DLP in the Jacobian variety of the covering curve which has higher genus over the smaller definition field. Gaudry et al.'s double-large-prime attack can be applied if the covering curve is a hyperelliptic curve and Diem's double-large-prime attack can be applied if the covering curve is non-hyperelliptic. It is known that attack to non-hyperelliptic curves is more efficient than to hyperelliptic curves. An important issue in the GHS attack is to construct the covering curve over $k$ explicitly.
Until now, two algorithms for non-hyperelliptic covering curves were shown by Diem and Hashizume, et al.. In this paper, we compare the two methods on the classes of the curves each method can be applied. Then Hashizume' method is generalized for genus two hyperelliptic cryptosystems. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
elliptic curve cryptosystems / GHS Attack / non-hyperelliptic curve / / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 110, no. 443, ISEC2010-96, pp. 143-150, March 2011. |
Paper # |
ISEC2010-96 |
Date of Issue |
2011-02-24 (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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IT2010-92 ISEC2010-96 WBS2010-71 |
Conference Information |
Committee |
ISEC IT WBS |
Conference Date |
2011-03-03 - 2011-03-04 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Osaka University |
Topics (in Japanese) |
(See Japanese page) |
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Paper Information |
Registration To |
ISEC |
Conference Code |
2011-03-ISEC-IT-WBS |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Construction of non-hyperelliptic coverings for elliptic curves on extension fields |
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Keyword(1) |
elliptic curve cryptosystems |
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GHS Attack |
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non-hyperelliptic curve |
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1st Author's Name |
Hiroyuki Hara |
1st Author's Affiliation |
Chuo University (Chuo Univ.) |
2nd Author's Name |
Tsutomu Iijima |
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3rd Author's Name |
Mahoro Shimura |
3rd Author's Affiliation |
Tokai University (Tokai Univ.) |
4th Author's Name |
Jinhui Chao |
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Chuo University (Chuo Univ.) |
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Speaker |
Author-1 |
Date Time |
2011-03-04 09:00:00 |
Presentation Time |
25 minutes |
Registration for |
ISEC |
Paper # |
IT2010-92, ISEC2010-96, WBS2010-71 |
Volume (vol) |
vol.110 |
Number (no) |
no.442(IT), no.443(ISEC), no.444(WBS) |
Page |
pp.143-150 |
#Pages |
8 |
Date of Issue |
2011-02-24 (IT, ISEC, WBS) |
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