Basic Properties of the (t, n)-Threshold Visual Secret Sharing Scheme with Perfect Reconstruction of Black Pixels |
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Authors: | Hiroki Koga Etsuyo Ueda |
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Institution: | (1) Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba Ibaraki, 305-8573, Japan |
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Abstract: | In this paper we consider the (t, n)-threshold visual secret sharing scheme (VSSS) in which black pixels in a secret black-white images is reproduced perfectly
as black pixels when we stack arbitrary t shares. This paper provides a new characterization of the (t, n)-threshold visual secret sharing scheme with such a property (hereafter, we call such a VSSS the (t, n)-PBVSSS for short). We use an algebraic method to characterize basis matrices of the (t, n)-PBVSSS in a certain class of matrices. We show that the set of all homogeneous polynomials each element of which yields
basis matrices of the (t, n)-PBVSSS becomes a set of lattice points in an (n−t+1)-dimensional linear space. In addition, we prove that the optimal basis matrices in the sense of maximizing the relative
difference among all the basis matrices in the class coincides with the basis matrices given by Blundo, Bonis and De Santis
3] for all n≥ t ≥ 2. |
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Keywords: | Visual cryptography Visual secret sharing Secret sharing Threshold scheme |
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