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Paper Abstract and Keywords
Presentation 2019-03-07 11:20
A Consideration of the Properties of Edwards Curve Whose Order is a Power of 2
Hiromasa Miura, Kazuya Kobayashi, Takuya Kusaka, Yasuyuki Nogami (Okayama Univ.) IT2018-79 ISEC2018-85 WBS2018-80
Abstract (in Japanese) (See Japanese page) 
(in English) Based on the proposal of pairing-based cryptography, ID-based cryptography, searchable cryptography, and attribute-based cryptography which could not be done by conventional cryptography are proposed. The efficiency of encryption and decryption in these cryptographies depend on the computational cost of scalar multiplication for points of the elliptic curve over a finite field. They will be improved by efficient scalar multiplication. Therefore, we consider on mapping from the pairing-friendly curve (BLS curve) to Twisted Edwards curve which has low-cost scalar multiplication in order to improve them. In this case, the Twisted Edwards curve has special parameters,sosomepointscannotbedefinedandtherearepointswhichcannotapplygeneralellipticcurveaddition or elliptic curve doubling. In this paper, we derive the Twisted Edwards curve with parameters that ECA and ECD are applied for all rational points when the order is a power of 2.
Keyword (in Japanese) (See Japanese page) 
(in English) BLS curve / Twisted Edwards curve / elliptic curve addition / elliptic curve doubling / / / /  
Reference Info. IEICE Tech. Rep., vol. 118, no. 478, ISEC2018-85, pp. 27-32, March 2019.
Paper # ISEC2018-85 
Date of Issue 2019-02-28 (IT, ISEC, WBS) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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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 IT ISEC WBS  
Conference Date 2019-03-07 - 2019-03-08 
Place (in Japanese) (See Japanese page) 
Place (in English) University of Electro-Communications 
Topics (in Japanese) (See Japanese page) 
Topics (in English) joint meeting of IT, ISEC, and WBS 
Paper Information
Registration To ISEC 
Conference Code 2019-03-IT-ISEC-WBS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Consideration of the Properties of Edwards Curve Whose Order is a Power of 2 
Sub Title (in English)  
Keyword(1) BLS curve  
Keyword(2) Twisted Edwards curve  
Keyword(3) elliptic curve addition  
Keyword(4) elliptic curve doubling  
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1st Author's Name Hiromasa Miura  
1st Author's Affiliation Okayama University (Okayama Univ.)
2nd Author's Name Kazuya Kobayashi  
2nd Author's Affiliation Okayama University (Okayama Univ.)
3rd Author's Name Takuya Kusaka  
3rd Author's Affiliation Okayama University (Okayama Univ.)
4th Author's Name Yasuyuki Nogami  
4th Author's Affiliation Okayama University (Okayama Univ.)
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Speaker Author-1 
Date Time 2019-03-07 11:20:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # IT2018-79, ISEC2018-85, WBS2018-80 
Volume (vol) vol.118 
Number (no) no.477(IT), no.478(ISEC), no.479(WBS) 
Page pp.27-32 
#Pages
Date of Issue 2019-02-28 (IT, ISEC, WBS) 


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