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Paper Abstract and Keywords
Presentation 2018-05-16 10:00
Hardness of Discrete Logarithm Problem Based on New Operation on Elliptic Curve over Finite Field and New Digital Signature
Masaaki Shirase (FUN) ISEC2018-1
Abstract (in Japanese) (See Japanese page) 
(in English) In the previous works, a new operation on elliptic curve over finite field $E(Fp)$, the Me operation $oplus$, is defined, and the Me scalar multiplication $P_{n,Z}$ for $P,Z in Fp$ and $n in N$ is defined. Moreover, the MeDLP (given $P,Z,P_{n,Z}$, compute $n$), the MeCDH (given $P_{n,Z}$ and $P_{m,Z}$, compute $(P_{n,Z})_{m,Z})$, and the modified MeCDH are defined. Although the MeCDH can be solved easily, the hardness of the MeDLP and the modified MeCDH were unknown. First, this report gives a solution of the modified MeCDH. Second, this report defines the MeDLP' as given $(P,z,P_{n,zP}) in E(Fp) times Z times E(Fp)$, compute $n in N$, and shows that the MeDLP' is as hard as, or harder than the ECDLP. Last, this report proposes a digital signature using the Me scalar multiplication.
Keyword (in Japanese) (See Japanese page) 
(in English) Elliptic curve cryptosystem / M operation / Me operation / Digital signature / Discrete logarithm problem / / /  
Reference Info. IEICE Tech. Rep., vol. 118, no. 30, ISEC2018-1, pp. 1-8, May 2018.
Paper # ISEC2018-1 
Date of Issue 2018-05-09 (ISEC) 
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 ISEC  
Conference Date 2018-05-16 - 2018-05-16 
Place (in Japanese) (See Japanese page) 
Place (in English) Ookayama Campus, Tokyo Institute of Technology 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To ISEC 
Conference Code 2018-05-ISEC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Hardness of Discrete Logarithm Problem Based on New Operation on Elliptic Curve over Finite Field and New Digital Signature 
Sub Title (in English)  
Keyword(1) Elliptic curve cryptosystem  
Keyword(2) M operation  
Keyword(3) Me operation  
Keyword(4) Digital signature  
Keyword(5) Discrete logarithm problem  
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1st Author's Name Masaaki Shirase  
1st Author's Affiliation Future University Hakodate (FUN)
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Speaker Author-1 
Date Time 2018-05-16 10:00:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # ISEC2018-1 
Volume (vol) vol.118 
Number (no) no.30 
Page pp.1-8 
#Pages
Date of Issue 2018-05-09 (ISEC) 


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