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Paper Abstract and Keywords
Presentation 2014-07-03 14:15
Security of RSA with Many Decryption Exponents
Atsushi Takayasu, Noboru Kunihiro (Univ. of Tokyo) ISEC2014-19 SITE2014-14 ICSS2014-23 EMM2014-19
Abstract (in Japanese) (See Japanese page) 
(in English) When we use small secret exponents, RSA becomes efficient for its decryption cost and signature generation cost. However, it is widly known that too small secret exponents enables attackers to factor RSA modulus N
efficiently. Boneh and Durfee used lattice based Coppersmith’s method and proposed polynomial time algorithm to factor the modulus when d < N^{1-1/sqrt{2}}. So far, the variants of the problem have been considered when there are k encryption/decryption exponents pairs. Howgrave-Graham and Seifert solved diophanine approximation problems and propsoed a polynomial time algorithm to factor RSA modulus. When k→∞, the algorithm works for even full size decryption exponents. Aono used the Coppersmith’s method and proposed an algorithm. Though Aono’s algorithm is better than the all previous ones for small k >= 2, when k = 1, the algorithm only works when d < N^{3/4}. In this paper, we use the Coppersmith’s method as Aono and propose improved algorithm. Our algorithm works when d < N^{1-2/(3k+1)}.
Keyword (in Japanese) (See Japanese page) 
(in English) RSA / Lattices / Coppersmith's method / / / / /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 115, ISEC2014-19, pp. 93-96, July 2014.
Paper # ISEC2014-19 
Date of Issue 2014-06-26 (ISEC, SITE, ICSS, EMM) 
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)
Download PDF ISEC2014-19 SITE2014-14 ICSS2014-23 EMM2014-19

Conference Information
Committee ICSS ISEC SITE EMM IPSJ-CSEC IPSJ-SPT  
Conference Date 2014-07-03 - 2014-07-04 
Place (in Japanese) (See Japanese page) 
Place (in English) San-Refure Hakodate 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Security 
Paper Information
Registration To ISEC 
Conference Code 2014-07-ICSS-ISEC-SITE-EMM-CSEC-SPT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Security of RSA with Many Decryption Exponents 
Sub Title (in English)  
Keyword(1) RSA  
Keyword(2) Lattices  
Keyword(3) Coppersmith's method  
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1st Author's Name Atsushi Takayasu  
1st Author's Affiliation The University of Tokyo (Univ. of Tokyo)
2nd Author's Name Noboru Kunihiro  
2nd Author's Affiliation The University of Tokyo (Univ. of Tokyo)
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Speaker Author-1 
Date Time 2014-07-03 14:15:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # ISEC2014-19, SITE2014-14, ICSS2014-23, EMM2014-19 
Volume (vol) vol.114 
Number (no) no.115(ISEC), no.116(SITE), no.117(ICSS), no.118(EMM) 
Page pp.93-96 
#Pages 4 
Date of Issue 2014-06-26 (ISEC, SITE, ICSS, EMM) 

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