A construction of the progressive (3, n)-threshold visual cryptography using a BIBD and analysis of its optimality

We consider a certain class of the (t, n)-threshold visual cryptography scheme called the (t, n)-PVCS in which quality of the reproduced image that appears by superimposition of more than or equal to t shares improves as the number of the superimposed shares increases. We first formulate a linear programming problem followed by an integer programming problem in order to maximize the relative difference caused by superimposition of all the n shares. Next, we propose a construction of the (3, n)-PVCS using the incident matrix of a BIBD. We also discuss the conditions for the BIBD under which the obtained pair of basis matrices becomes optimal.