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Paper Abstract and Keywords
Presentation 2026-03-17 09:00
A Tight Upper Bound of the Optimal Relative Difference of Superimposed All the Shares for a (3,n)-Threshold Visual Cryptography
Hiroki Koga, Naoki Mitarai (Univ. Tsukuba) IT2025-104 ISEC2025-112 WBS2025-86 RCC2025-85
Abstract (in Japanese) (See Japanese page) 
(in English) A (t,n)-threshold visual cryptography scheme ((t,n)-VCS for short) provides a nonconventional secret sharing scheme for digital black-white images. In the (t,n)-VCS, a dealer generates n shares from a secret image, prints each share on a transparency sheet, and distributes the printed n shares to the respective n participants. While t arbitrary participants can recover the secret image by superimposition of their shares, no information on the secret image is revealed from any less than t shares. In this paper, we focus on the total relative difference that represents the contrast between black and white pixels in the image obtained by superimposing all the n shares. We succeed in obtaining a tight upper bound of the total relative difference for the case of t=3 by using a combinatorial argument. This upper bound leads to the optimal construction of the (3,n)-VCS using a BIBD.
Keyword (in Japanese) (See Japanese page) 
(in English) visual cryptography / threshold scheme / relative difference / pixel expansion / / / /  
Reference Info. IEICE Tech. Rep., vol. 125, no. 404, IT2025-104, pp. 157-162, March 2026.
Paper # IT2025-104 
Date of Issue 2026-03-09 (IT, ISEC, WBS, RCC) 
ISSN 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 IT2025-104 ISEC2025-112 WBS2025-86 RCC2025-85

Conference Information
Committee IT WBS ISEC RCC  
Conference Date 2026-03-16 - 2026-03-17 
Place (in Japanese) (See Japanese page) 
Place (in English) Nagano Campus, Shinshu University 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Joint Workshop of ISEC, IT, RCC, and WBS 
Paper Information
Registration To IT 
Conference Code 2026-03-IT-WBS-ISEC-RCC 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A Tight Upper Bound of the Optimal Relative Difference of Superimposed All the Shares for a (3,n)-Threshold Visual Cryptography 
Sub Title (in English)  
Keyword(1) visual cryptography  
Keyword(2) threshold scheme  
Keyword(3) relative difference  
Keyword(4) pixel expansion  
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1st Author's Name Hiroki Koga  
1st Author's Affiliation University of Tsukuba (Univ. Tsukuba)
2nd Author's Name Naoki Mitarai  
2nd Author's Affiliation University of Tsukuba (Univ. Tsukuba)
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Speaker Author-1 
Date Time 2026-03-17 09:00:00 
Presentation Time 25 minutes 
Registration for IT 
Paper # IT2025-104, ISEC2025-112, WBS2025-86, RCC2025-85 
Volume (vol) vol.125 
Number (no) no.404(IT), no.405(ISEC), no.406(WBS), no.407(RCC) 
Page pp.157-162 
#Pages 6 
Date of Issue 2026-03-09 (IT, ISEC, WBS, RCC) 

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