Constructions and properties of \(k\) out of \(n\) visual secret sharing schemes
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.
scientific article; zbMATH DE number 1028925