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| Presentation | 2008-02-28 17:45 A Study on Efficient Scalar Multiplication for Elliptic Curve Cryptosystems Naoya Terashima, Tomoko K. Matsushima, Osamu Ashihara (Polytechnic Univ.)  IT2007-41 ISEC2007-138 WBS2007-72 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Efficient elliptic curve arithmetic is crucial for cryptosystems based on elliptic curves. Such cryptosystems often require computing a scalar multiple $kP$ of a base point $P$. Recently, some papers propose efficient algorithms to compute $\lambda P \pm \mu Q$ directly for small integers $\lambda$ and $\mu$ from given points $P$ and $Q$. We develop some programs to find the path with the minimum cost for each scalar multiplication $kP$ under the condition that several operations of $\lambda P \pm \mu Q$ can be used with relatively small costs. We have construct the minimum-cost path table in which the maximum number of $k$ ($k_{max}$) is around $10^5$ ($2^{18}$). We also show some algorithms to compute $KP$ where $k_{max} \ll K$. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | elliptic curves / scalar multiplication / addition chains / power tree / path table / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 107, no. 500, ISEC2007-138, pp. 59-66, Feb. 2008. | |
| Paper # | ISEC2007-138 | |
| Date of Issue | 2008-02-21 (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 | IT2007-41 ISEC2007-138 WBS2007-72 |
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| Conference Information | |
| Committee | ISEC IT WBS |
| Conference Date | 2008-02-28 - 2008-02-29 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | ISEC |
| Conference Code | 2008-02-ISEC-IT-WBS |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A Study on Efficient Scalar Multiplication for Elliptic Curve Cryptosystems |
| Sub Title (in English) | |
| Keyword(1) | elliptic curves |
| Keyword(2) | scalar multiplication |
| Keyword(3) | addition chains |
| Keyword(4) | power tree |
| Keyword(5) | path table |
| Keyword(6) | |
| Keyword(7) | |
| Keyword(8) | |
| 1st Author's Name | Naoya Terashima |
| 1st Author's Affiliation | Polytechnic University (Polytechnic Univ.) |
| 2nd Author's Name | Tomoko K. Matsushima |
| 2nd Author's Affiliation | Polytechnic University (Polytechnic Univ.) |
| 3rd Author's Name | Osamu Ashihara |
| 3rd Author's Affiliation | Polytechnic University (Polytechnic Univ.) |
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| Speaker | Author-1 |
| Date Time | 2008-02-28 17:45:00 |
| Presentation Time | 25 minutes |
| Registration for | ISEC |
| Paper # | IT2007-41, ISEC2007-138, WBS2007-72 |
| Volume (vol) | vol.107 |
| Number (no) | no.498(IT), no.500(ISEC), no.502(WBS) |
| Page | pp.59-66 |
| #Pages | 8 |
| Date of Issue | 2008-02-21 (IT, ISEC, WBS) |
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