Paper Abstract and Keywords |
Presentation |
2008-05-16 14:40
A Study on Higher Order Differnce Operation for Elliptic Curve Scalar Multiplication Using Path Table Tomoko K. Matsushima, Yoshitaka Sagara, Osamu Ashihara (Polytechnic Univ.) ISEC2008-11 |
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 have proposed efficient algorithms to compute $\lambda P \pm \mu Q$ directly for small integers $\lambda$ and $\mu$ from given points $P$ and $Q$. The authors have already developed 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. We have also developed the minimum-cost path-table of scalar multiples $kP$ for $1 \le k \le k_{max}$.
In this paper, we present an algorithm to compute $KP$ where $k_{max} \ll K$. The algorithm adopts the higher order difference operation for the coefficients in $b$-ary representation of $KP$ where $b$ is the radix. We evaluate the costs due to our proposed algorithm in comparison with some
conventional algorithms. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
elliptic curves / scalar multiplication / addition chains / power tree / path table / higher order difference operation / / |
Reference Info. |
IEICE Tech. Rep., vol. 108, no. 38, ISEC2008-11, pp. 69-76, May 2008. |
Paper # |
ISEC2008-11 |
Date of Issue |
2008-05-09 (ISEC) |
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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ISEC2008-11 |
Conference Information |
Committee |
ISEC |
Conference Date |
2008-05-16 - 2008-05-16 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Kikai-Shinko-Kaikan Bldg. |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
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Paper Information |
Registration To |
ISEC |
Conference Code |
2008-05-ISEC |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
A Study on Higher Order Differnce Operation for Elliptic Curve Scalar Multiplication Using Path Table |
Sub Title (in English) |
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Keyword(1) |
elliptic curves |
Keyword(2) |
scalar multiplication |
Keyword(3) |
addition chains |
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power tree |
Keyword(5) |
path table |
Keyword(6) |
higher order difference operation |
Keyword(7) |
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1st Author's Name |
Tomoko K. Matsushima |
1st Author's Affiliation |
Polytechnic University (Polytechnic Univ.) |
2nd Author's Name |
Yoshitaka Sagara |
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 |
2008-05-16 14:40:00 |
Presentation Time |
25 minutes |
Registration for |
ISEC |
Paper # |
ISEC2008-11 |
Volume (vol) |
vol.108 |
Number (no) |
no.38 |
Page |
pp.69-76 |
#Pages |
8 |
Date of Issue |
2008-05-09 (ISEC) |