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Paper Abstract and Keywords
Presentation 2014-03-11 11:25
A Distribution Related to The Exponentiation Inversion Problem Reduced from Fixed Argument Pairing Inversion 2 Problem over Barreto-Naehrig Curve
Shoichi Akagi, Yasuyuki Nogami (Okayama Univ.) IT2013-80 ISEC2013-109 WBS2013-69
Abstract (in Japanese) (See Japanese page) 
(in English) As one of problems that guarantee the security of pairing--based cryptography, {em pairing inversion} problem is studied.
The pairing inversion problem is classified into three types as {em fixed argument pairing inversion--1} (FAPI) ploblem, FAPI--2 problem, General Pairing Inversion (GPI) problem.
Some recent works have reduced {em fixed argument pairing inversion} (FAPI) ploblem to exponentiation inversion (EI) problem. According to the results, FAPI problem is solved if EI problem of exponent $(q^k-1)/{rm Phi}_k(q)$ is solved, where $q$, $k$, and $r$ are the characteristic, embedding degree, and order of pairing group, respectively. ${rm Phi}_k(x)$ is the cyclotomic polynomial of order $k$.
In addition, it is shown that FAPI--2 on Tate pairing using Barreto--Naehrig curve is reduced to $(q-1)$--th EI problem.
However, the problem is still difficult. Thus, this paper shows the difficulty by examining a certain distribution related to the EI problem over F{q}{}.
Keyword (in Japanese) (See Japanese page) 
(in English) Pairing / Pairing Inversion Problem / FAPI / Barreto--Naehrig curve / / / /  
Reference Info. IEICE Tech. Rep., vol. 113, no. 484, ISEC2013-109, pp. 163-168, March 2014.
Paper # ISEC2013-109 
Date of Issue 2014-03-03 (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)
Download PDF IT2013-80 ISEC2013-109 WBS2013-69

Conference Information
Committee ISEC IT WBS  
Conference Date 2014-03-10 - 2014-03-11 
Place (in Japanese) (See Japanese page) 
Place (in English) Nagoya Univ., Higashiyama Campus 
Topics (in Japanese) (See Japanese page) 
Topics (in English) joint meeting of IT, ISEC, and WBS 
Paper Information
Registration To ISEC 
Conference Code 2014-03-ISEC-IT-WBS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Distribution Related to The Exponentiation Inversion Problem Reduced from Fixed Argument Pairing Inversion 2 Problem over Barreto-Naehrig Curve 
Sub Title (in English)  
Keyword(1) Pairing  
Keyword(2) Pairing Inversion Problem  
Keyword(3) FAPI  
Keyword(4) Barreto--Naehrig curve  
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1st Author's Name Shoichi Akagi  
1st Author's Affiliation Okayama University (Okayama Univ.)
2nd Author's Name Yasuyuki Nogami  
2nd Author's Affiliation Okayama University (Okayama Univ.)
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Speaker Author-1 
Date Time 2014-03-11 11:25:00 
Presentation Time 25 minutes 
Registration for ISEC 
Paper # IT2013-80, ISEC2013-109, WBS2013-69 
Volume (vol) vol.113 
Number (no) no.483(IT), no.484(ISEC), no.485(WBS) 
Page pp.163-168 
#Pages 6 
Date of Issue 2014-03-03 (IT, ISEC, WBS) 

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