On the Relation of Random Grid and Deterministic Visual Cryptography

Visual cryptography is a special type of secret sharing. Two models of visual cryptography have been independently studied: 1) deterministic visual cryptography, introduced by Naor and Shamir, and 2) random grid visual cryptography, introduced by Kafri and Keren. In this paper, we show that there is a strict relation between these two models. In particular, we show that to any random grid scheme corresponds a deterministic scheme and vice versa. This allows us to use results known in a model also in the other model. By exploiting the (many) results known in the deterministic model, we are able to improve several schemes and to provide many upper bounds for the random grid model and by exploiting some results known for the random grid model, we are also able to provide new schemes for the deterministic model. A side effect of this paper is that future new results for any one of the two models should not ignore, and in fact be compared with, the results known in the other model.