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Paper Abstract and Keywords
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
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

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  
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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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