A novel (t, s, k, n)-threshold visual secret sharing scheme based on access structure partition

Visual secret sharing (VSS) is a new technique for sharing a binary image into multiple shadows. For VSS, the original image can be reconstructed from the shadows in any qualified set, but cannot be reconstructed from those in any forbidden set. In most traditional VSS schemes, the shadows held by participants have the same importance. However, in practice, a certain number of shadows are given a higher importance due to the privileges of their owners. In this article, a novel (t, s, k, n)-threshold VSS scheme is proposed based on access structure partition. First, we construct the basis matrix of the proposed (t, s, k, n)-threshold VSS scheme by utilizing a new access structure partition method and sub-access structure merging method. Then, the secret image is shared by the basis matrix as n shadows, which are divided into s essential shadows and n - s non-essential shadows. To reconstruct the secret image, k or more shadows should be collected, which include at least t essential shadows; otherwise, no information about the secret image can be obtained. Compared with related schemes, our scheme achieves a smaller shadow size and a higher visual quality of the reconstructed image. Theoretical analysis and experiments indicate the effectiveness of the proposed scheme.