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Paper Abstract and Keywords
Presentation 2015-09-04 10:30
Improved addition algorithm for Edwards Curve
Masaaki Shirase (Future Univ Hakodate) ISEC2015-25
Abstract (in Japanese) (See Japanese page) 
(in English) This paper introduces a new coordinate system (named ${cal P}times {cal P}$ coordinate system) in which a point $(x,y)$ in affine is represented as $[X,Y,Z,W]$ satisfying $x=X/Z,y=Y/W$ and then proposes new algorithms for computing addition and duplication on Edwards curve $x^2+y^2=1+dx^2y^2$. Given $P$ in ${cal P}times {cal P}$ and $Q$ in affine, $P+Q$ and $2P$ take 8{bf M} and 3{bf M}+4{bf S}, respectively, where $M$ and $S$ are multiplication and squaring cost. This paper also proposes algorithms for computing addtion and duplication on twisted Edwards curve $ax^2+y^2=1+dx^2y^2$. Addition takes 9{bf M}, or 7{bf M} when $a=-1$. Duplication takes 6{cal M}+3{cal S}, or 3{bf M}+4{cal S} when $a=-1$.
Keyword (in Japanese) (See Japanese page) 
(in English) elliptic curve cryptosystem / Edwards curve / addition algorithm / coordinate system / / / /  
Reference Info. IEICE Tech. Rep., vol. 115, no. 215, ISEC2015-25, pp. 1-8, Sept. 2015.
Paper # ISEC2015-25 
Date of Issue 2015-08-28 (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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Conference Information
Committee ISEC  
Conference Date 2015-09-04 - 2015-09-04 
Place (in Japanese) (See Japanese page) 
Place (in English) Kikai-Shinko-Kaikan Bldg. 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To ISEC 
Conference Code 2015-09-ISEC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Improved addition algorithm for Edwards Curve 
Sub Title (in English)  
Keyword(1) elliptic curve cryptosystem  
Keyword(2) Edwards curve  
Keyword(3) addition algorithm  
Keyword(4) coordinate system  
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1st Author's Name Masaaki Shirase  
1st Author's Affiliation Future University Hakodate (Future Univ Hakodate)
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Speaker Author-1 
Date Time 2015-09-04 10:30:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # ISEC2015-25 
Volume (vol) vol.115 
Number (no) no.215 
Page pp.1-8 
#Pages 8 
Date of Issue 2015-08-28 (ISEC) 

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