Imagine you have several transparencies and they all have black and white regions or pixels. Each one of them may not show anything in particular, but stacked up, an image may be revealed. This is the gist of a visual cryptography scheme (VCS). In a (k, n)-VCS (2 ≤ k ≤ n), any set of less than k transparencies cannot reveal the image.

Several theorems are given that lead to two algorithms for constructing VCSs. One approach known in the literature is based on a cumulative array method. The second method is recursive in both the n and k parameters. The research presented gives several lower and upper bounds, laying the groundwork for shortcuts in the algorithms’ analyses, which will hopefully appear in an upcoming paper.

The paper is easy to follow due to the examples, and structured well so that readers can easily follow the exposition. While it may appear at first that this is a paper for mathematicians only, the examples make the research easy for nonmathematicians to understand.

So, we can hide a message with layers of transparencies and as long as one carrier does not have too many, the secret message will remain secret up until the time when a minimum of k of them are in one place.