Constructions and properties of \(k\) out of \(n\) visual secret sharing schemes
type: Item
instance of: scholarly article
title: Constructions and properties of \(k\) out of \(n\) visual secret sharing schemes
zbMATH Open document ID: 0878.94049
DOI: 10.1023/A:1008280705142
author: Eric R. Verheul
author: Henk van Tilborg
published in: Designs, Codes and Cryptography
publication date: 1997-12-18T00:00:00Z
review text: The notion of secret sharing schemes for images is considered. Each pixel of an original image is divided into \(b\) subpixels, each subpixel either white or black. The image is transformed into \(n\) transparencies or shares, in such a way that if any \(k\)-tuple of transparencies are overlaid, the original image is again, visible. It is assumed a pixel, (the total of the \(b\) subpixels) will be observed as white if at least \(h\) of the subpixels are white and black if at most \(l\) of them are white, for some suitable positive integers \(h>l\). These notions were introduced by \textit{M. Naor} and \textit{A. Shamir} [Lect. Notes Comput. Sci. 950, 1-11 (1994; Zbl 0878.94048)], who also gave constructions for the cases of \(k=2\) and \(k=n\). This paper gives two general constructions for \(k\) out of \(n\) schemes. The parameters of the schemes are related to those of maximum arcs or MDS codes. Results on the structure of such schemes, including bounds on their parameters, are obtained. An extension of the notion to coloured visual secret sharing schemes is introduced and a general construction given.
reviewed by: Ian Blake
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 68P25
zbMATH DE Number: 1028925
zbMATH Keywords: visual cryptography
zbMATH Keywords: secret sharing schemes
zbMATH Keywords: MDS codes
zbMATH Keywords: arcs
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1028925