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| Presentation | 2015-03-02 15:35 Analysis on isomorphism classes of elliptic curves subjected to GHS attack over prime degree extensions of finite fields with odd characteristic Takayuki Hosogaya (Chuo Univ.), Tsutomu Iijima (Koden), Mahoro Shimura (Tokai Univ.), Jinhui Chao (Chuo Univ.)  IT2014-76 ISEC2014-89 WBS2014-68 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | The GHS attack is known to map the discrete logarithm problem (DLP) in the Jacobian of a curve $C_0$ defined over the $d$ degree extension $k_d$ of a finite field $k$ to the DLP in the Jacobian of a new curve $C$ over $k$ which is a covering curve of $C_0$. Recently, classification of all elliptic curves possessing (2,...,2) covering $C$ therefore subjected to the GHS attack is obtained in [27]. However, a such curve $C_0$ could be mapped by an $k_d$-isomorphism to another curve which also possesses a covering curve but with a different genus. In this paper, we present a detailed analysis on $k_d$-isomorphic classes of these curves. In particular, we show orbit-decomposition of them under action of PGL$(2,k_d)$ in case of $d=2$. Security against GHS attack of a curve $C_0$ is evaluated according to all possible genera $g(C)$ among the curves belong to the PGL-orbit |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Elliptic Curve Cryptography / GHS attack / / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 114, no. 471, ISEC2014-89, pp. 89-95, March 2015. | |
| Paper # | ISEC2014-89 | |
| Date of Issue | 2015-02-23 (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) | |
| Download PDF | IT2014-76 ISEC2014-89 WBS2014-68 |
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| Conference Information | |
| Committee | ISEC IT WBS |
| Conference Date | 2015-03-02 - 2015-03-03 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | The University of Kitakyushu |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | joint meeting of IT, ISEC, and WBS |
| Paper Information | |
| Registration To | ISEC |
| Conference Code | 2015-03-ISEC-IT-WBS |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Analysis on isomorphism classes of elliptic curves subjected to GHS attack over prime degree extensions of finite fields with odd characteristic |
| Sub Title (in English) | |
| Keyword(1) | Elliptic Curve Cryptography |
| Keyword(2) | GHS attack |
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| 1st Author's Name | Takayuki Hosogaya |
| 1st Author's Affiliation | Chuo University (Chuo Univ.) |
| 2nd Author's Name | Tsutomu Iijima |
| 2nd Author's Affiliation | Koden Electronics Co., Ltd (Koden) |
| 3rd Author's Name | Mahoro Shimura |
| 3rd Author's Affiliation | Tokai University (Tokai Univ.) |
| 4th Author's Name | Jinhui Chao |
| 4th Author's Affiliation | Chuo University (Chuo Univ.) |
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| Speaker | Author-1 |
| Date Time | 2015-03-02 15:35:00 |
| Presentation Time | 25 minutes |
| Registration for | ISEC |
| Paper # | IT2014-76, ISEC2014-89, WBS2014-68 |
| Volume (vol) | vol.114 |
| Number (no) | no.470(IT), no.471(ISEC), no.472(WBS) |
| Page | pp.89-95 |
| #Pages | 7 |
| Date of Issue | 2015-02-23 (IT, ISEC, WBS) |
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