An easy-to-implement construction for [formula omitted]-threshold progressive visual secret sharing schemes.

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, which have been showed equivalent in some sense, in the literature: codebook-based schemes and random-grid-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. • The resulting scheme has a progressive-viewing property that means the more shares being stacked together the clearer the secret image would be revealed. • The proposed scheme can be constructed explicitly and efficiently based on the generalized Pascal's triangle without a computer. • Performance of the proposed scheme is comparable with known results. [ABSTRACT FROM AUTHOR]