Polynomial Representation of a Visual Secret Sharing Scheme and Its Application

Hidenori KUWAKADO  Hatsukazu TANAKA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A   No.6   pp.1379-1386
Publication Date: 2002/06/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Security
information security,  visual secret sharing,  polynomial representation,  

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A visual secret sharing scheme (VSSS) is one of secret sharing schemes for images. Droste showed the method for constructing VSSS based on basis matrices whose contrast was high. Koga, Iwamoto, and Yamamoto also proposed the method for constructing a lattice-based VSSS and its polynomial representation. It is known that many good VSSSs are not in the class of lattice-based VSSSs. In this paper, we show the well-defined polynomial representation of a VSSS based on permuting different matrices for black-white images. The necessary and sufficient condition of the existence of a VSSS based on permuting different matrices can be obtained from the proposed polynomial representation. This condition is useful for constructing a good VSSS. We also point out that without additional data, it is possible to achieve member verification by using a VSSS. Using the proposed polynomial representation, the probability of detecting a cheater is analyzed.