An Easy-to-implement Construction for $(k,n)$-threshold Progressive Visual Secret Sharing Schemes

Abstract

Visual cryptography encrypts the secret image into n shares (transparency) so that only stacking a qualified number of shares can recover the secret image by the human visual system while no information can be revealed without a large enough number of shares. This paper investigates the (k, n)-threshold Visual Secret Sharing (VSS) model, where one can decrypt the original image by stacking at least k shares and get nothing with less than k shares. There are two main approaches in the literature: codebook-based schemes and randomgrid-based schemes; the former is the case of this paper. In general, given any positive integers k and n, it is not easy to design a valid scheme for the (k, n)threshold VSS model. In this paper, we propose a simple strategy to construct an efficient scheme for the (k, n)-threshold VSS model for any positive integers 2 ≤ k ≤ n. The crucial idea is to establish a seemingly unrelated connection between the (k, n)-threshold VSS scheme and a mathematical structure -the generalized Pascal's triangle. This paper improves and extends previous results in four aspects:• Our construction offers a unified viewpoint and covers several known results;