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Paper Abstract and Keywords
Presentation 2015-03-02 14:05
On the Limit of Security Proof for Homomorphic Encryption
Daiki Takahashi, Shingo Hasegawa, Shuji Isobe, Eisuke Koizumi, Hiroki Shizuya (Tohoku Univ.) IT2014-67 ISEC2014-80 WBS2014-59
Abstract (in Japanese) (See Japanese page) 
(in English) In this paper, we explore on the limitation of security proofs for homomorphic encryptions.
We consider the computational complexity for verifying the validity of the plaintext-ciphertext pairs, that is, on any given pair $(b,c)$, to determine whether or not $c$ is a ciphertext of the plaintext $b$.
We show that for any homomorphic encryption scheme, if the complexity of its verification problem is characterized by the classes in the low hierarchy within $mathbf{NP}$, then the scheme cannot be proven to be secure beyond the low hierarchy classes via reduction proofs.
We also discuss the case where the complexity of the verification problem is characterized by $SZK$, the class of languages that have statistical zero-knowledge proofs, and show that the limitation of the security proofs is characterized by some intermediate class between $SZK$ and $AMcapcoAM$.
Keyword (in Japanese) (See Japanese page) 
(in English) homomorphic encryption / security proof / low hierarchy / statistical zero-knowledge / / / /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 471, ISEC2014-80, pp. 33-38, March 2015.
Paper # ISEC2014-80 
Date of Issue 2015-02-23 (IT, ISEC, WBS) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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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 IT2014-67 ISEC2014-80 WBS2014-59

Conference Information
Committee ISEC IT WBS  
Conference Date 2015-03-02 - 2015-03-03 
Place (in Japanese) (See Japanese page) 
Place (in English) The University of Kitakyushu 
Topics (in Japanese) (See Japanese page) 
Topics (in English) joint meeting of IT, ISEC, and WBS 
Paper Information
Registration To ISEC 
Conference Code 2015-03-ISEC-IT-WBS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) On the Limit of Security Proof for Homomorphic Encryption 
Sub Title (in English)  
Keyword(1) homomorphic encryption  
Keyword(2) security proof  
Keyword(3) low hierarchy  
Keyword(4) statistical zero-knowledge  
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1st Author's Name Daiki Takahashi  
1st Author's Affiliation Tohoku University (Tohoku Univ.)
2nd Author's Name Shingo Hasegawa  
2nd Author's Affiliation Tohoku University (Tohoku Univ.)
3rd Author's Name Shuji Isobe  
3rd Author's Affiliation Tohoku University (Tohoku Univ.)
4th Author's Name Eisuke Koizumi  
4th Author's Affiliation Tohoku University (Tohoku Univ.)
5th Author's Name Hiroki Shizuya  
5th Author's Affiliation Tohoku University (Tohoku Univ.)
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Speaker Author-1 
Date Time 2015-03-02 14:05:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # IT2014-67, ISEC2014-80, WBS2014-59 
Volume (vol) vol.114 
Number (no) no.470(IT), no.471(ISEC), no.472(WBS) 
Page pp.33-38 
#Pages
Date of Issue 2015-02-23 (IT, ISEC, WBS) 


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