A general method for construction of (t, n)-threshold visual secret sharing schemes for color images

作者：Koga Hiroki^*; Ishihara Takeru

来源：Designs, Codes and Cryptography, 2011, 61(2): 223-249.

DOI：10.1007/s10623-010-9449-x

• Visual cryptography
• Visual secret sharing
• Threshold scheme
• Contrast

This paper is concerned with the construction of basis matrices of visual secret sharing schemes for color images under the (t, n)-threshold access structure, where n a parts per thousand yen t a parts per thousand yen 2 are arbitrary integers. We treat colors as elements of a bounded semilattice and regard stacking two colors as the join of the two corresponding elements. We generate n shares from a secret image with K colors by using K matrices called basis matrices. The basis matrices considered in this paper belong to a class of matrices each element of which is represented by a homogeneous polynomial of degree n. We first clarify a condition such that the K matrices corresponding to K homogeneous polynomials become basis matrices. Next, we give an algebraic scheme for the construction of basis matrices. It is shown that under the (t, n)-threshold access structure we can obtain K basis matrices from appropriately chosen K - 1 homogeneous polynomials of degree n by using simple algebraic operations. In particular, we give basis matrices that are unknown so far for the cases of t = 2, 3 and n - 1.

• 出版日期2011-11