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Visual cryptography encrypts the secret image into $n$ shares (transparency)so that only stacking a qualified number of shares can recover the secret imageby the human visual system while no information can be revealed without a largeenough number of shares. This paper investigates the $(k,n)$-threshold VisualSecret Sharing (VSS) model, where one can decrypt the original image bystacking at least $k$ shares and get nothing with less than $k$ shares. Thereare two main approaches in the literature: codebook-based schemes andrandom-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 validscheme for the $(k,n)$-threshold VSS model. In this paper, we propose a simplestrategy to construct an efficient scheme for the $(k,n)$-threshold VSS modelfor any positive integers $2\leq k\leq n$. The crucial idea is to establish aseemingly unrelated connection between the $(k,n)$-threshold VSS scheme and amathematical structure -- the generalized Pascal's triangle. This paperimproves and extends previous results in four aspects: Our construction offersa unified viewpoint and covers several known results;  The resulting scheme has a progressive-viewing property that means the moreshares being stacked together the clearer the secret image would be revealed.  The proposed scheme can be constructed explicitly and efficiently based onthe generalized Pascal's triangle without a computer. Performance of theproposed scheme is comparable with known results.

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