Paper Abstract and Keywords |
Presentation |
2017-03-09 14:00
Security Analysis of Ordinary Isogeny Diffie--Hellman Satoshi Furukawa, Atsushi Takayasu, Noboru Kunihiro (The Univ. of Tokyo) IT2016-104 ISEC2016-94 WBS2016-80 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
In this paper, we analyze the security of Ordinary Isogeny Diffie--Hellman (OIDH) key exchange proposed by Stolbunov (Adv. Math. Commun. 2010). In particular, we consider a problem to compute the OIDH shared key from partial information (e.g. most significant bits) on the shared key. First, we define the Isogeny Hidden Number Problem (IHNP) which proposed by Galbraith {it et al.} (Asiacrypt 2016) for ordinary elliptic curves. Next, we propose the algorithm to solve IHNP for ordinary elliptic curves in polynomial time by using Coppersmith's method (Eurocrypt'96) for finding roots of modular equations. Our algorithm can recover the entire OIDH shared key in polynomial time if we get more than $6/7$ most significant bits of the shared key. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
Elliptic curve / Isogeny / OIDH key exchange / Coppersmith's method / / / / |
Reference Info. |
IEICE Tech. Rep., vol. 116, no. 505, ISEC2016-94, pp. 33-40, March 2017. |
Paper # |
ISEC2016-94 |
Date of Issue |
2017-03-02 (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) |
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IT2016-104 ISEC2016-94 WBS2016-80 |
Conference Information |
Committee |
ISEC WBS IT |
Conference Date |
2017-03-09 - 2017-03-10 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
TOKAI University |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
joint meeting of IT, ISEC, and WBS |
Paper Information |
Registration To |
ISEC |
Conference Code |
2017-03-ISEC-WBS-IT |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
Security Analysis of Ordinary Isogeny Diffie--Hellman |
Sub Title (in English) |
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Keyword(1) |
Elliptic curve |
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Isogeny |
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OIDH key exchange |
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Coppersmith's method |
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1st Author's Name |
Satoshi Furukawa |
1st Author's Affiliation |
The University of Tokyo (The Univ. of Tokyo) |
2nd Author's Name |
Atsushi Takayasu |
2nd Author's Affiliation |
The University of Tokyo (The Univ. of Tokyo) |
3rd Author's Name |
Noboru Kunihiro |
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The University of Tokyo (The Univ. of Tokyo) |
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Speaker |
Author-1 |
Date Time |
2017-03-09 14:00:00 |
Presentation Time |
25 minutes |
Registration for |
ISEC |
Paper # |
IT2016-104, ISEC2016-94, WBS2016-80 |
Volume (vol) |
vol.116 |
Number (no) |
no.504(IT), no.505(ISEC), no.506(WBS) |
Page |
pp.33-40 |
#Pages |
8 |
Date of Issue |
2017-03-02 (IT, ISEC, WBS) |
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