Proposal of a lattice-based visual secret sharing scheme for color and gray-scale images

The visual secret sharing scheme (VSSS) proposed by Naor and Shamir[1] provides a way to encrypt a secret black-white image into shares and decrypt the shares without using any cryptographic computation. This paper proposes an extension of VSSS to sharing of color or gray-scale images. In this paper (k, n) VSSS for images with J different colors is defined as a collection of J disjoint subsets in n-th product of a finite lattice. The subsets can be sequentially constructed as a solution of a certain simultaneous linear equation. In particular, the subsets are simply expressed in (n: n), (n - 1, n) and (2, n) cases. Any collections of ic - 1 shares reveal no information on a secret image while stacking of k arbitrary shares reproduces the secret image.