The aim of our paper is to show how Partially Balanced Incomplete Block Designs (PBIBD) may be used to construct (2,n) visual cryptographic schemes for black and white images with small pixel expansion. In situations where uniformity of the participants with respect to the relative contrast is not important, our schemes work well since by allowing the relative contrast to vary depending on which two participants are recovering the image, they can keep the pixel expansion quite small. Thus our schemes have considerably smaller pixel expansion than many of the existing schemes. For some n and some pairs of participants recovering the image, our schemes have larger relative contrast than some existing schemes.

Combinatorial designs are normally used to construct visual cryptographic schemes. For such schemes two parameters are very important viz. pixel expansion and contrast. Optimizing both is a very hard problem. The schemes having optimal contrast tend to use a high pixel expansion. The focus of the paper is to construct schemes for which pixel expansion is modest and the contrast is close to optimality. Here the tool is latin squares that haven't been used earlier for this purpose.