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Paper Abstract and Keywords
Presentation 2018-03-08 11:15
Construction of Secret Sharing Schemes with Small Thresholds for Countably Infinite Participants
Takashi Hisatome, Hiroki Koga (Univ. Tsukuba) IT2017-108 ISEC2017-96 WBS2017-89
Abstract (in Japanese) (See Japanese page) 
(in English) In Shamir's (k, n)-threshold scheme, given a secret S
a dealer generates n shares by using a random polynomial
of degree k-1 over a finite field Fq.
While S is recovered from arbitrary collection of more than
or equal to k shares, no information about S is revealed
from any collection of less than k shares.
In Shamir's scheme the number of shares is at most q-1.
Recently, Komargodski et al give a construction of a secret sharing scheme
called the evolving k-THR in which for a given secret S a dealer can generate countably infinite shares
with the property similar to Shamir's (k,n)-threshold scheme.
In this paper, we propose new simple constructions of
the evolving 3-THR and 4-THR and evaluate the sizes of the shares.
In particular, we prove that the size of the share of the t-th participant
can be reduced to O((log log t)^2) in the evolving 3-THR.
Keyword (in Japanese) (See Japanese page) 
(in English) secret sharing schemes / evolving k-THRs / / / / / /  
Reference Info. IEICE Tech. Rep., vol. 117, no. 487, IT2017-108, pp. 31-36, March 2018.
Paper # IT2017-108 
Date of Issue 2018-03-01 (IT, ISEC, WBS) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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 IT2017-108 ISEC2017-96 WBS2017-89

Conference Information
Committee WBS IT ISEC  
Conference Date 2018-03-08 - 2018-03-09 
Place (in Japanese) (See Japanese page) 
Place (in English) Katsusika Campas, Tokyo University of Science 
Topics (in Japanese) (See Japanese page) 
Topics (in English) joint meeting of IT, ISEC, and WBS 
Paper Information
Registration To IT 
Conference Code 2018-03-WBS-IT-ISEC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Construction of Secret Sharing Schemes with Small Thresholds for Countably Infinite Participants 
Sub Title (in English)  
Keyword(1) secret sharing schemes  
Keyword(2) evolving k-THRs  
1st Author's Name Takashi Hisatome  
1st Author's Affiliation University of Tsukuba (Univ. Tsukuba)
2nd Author's Name Hiroki Koga  
2nd Author's Affiliation University of Tsukuba (Univ. Tsukuba)
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Speaker Author-1 
Date Time 2018-03-08 11:15:00 
Presentation Time 25 minutes 
Registration for IT 
Paper # IT2017-108, ISEC2017-96, WBS2017-89 
Volume (vol) vol.117 
Number (no) no.487(IT), no.488(ISEC), no.489(WBS) 
Page pp.31-36 
Date of Issue 2018-03-01 (IT, ISEC, WBS) 

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