Visual Cryptography II: Improving the Contrast Via the Cover Base

In Eurocrypt'94 [3] we proposed a a new type of cryptographic scheme, which can decode concealed images without any cryptographic computations, by placing two transparencies on top of each other and using the decoder's (human) visual systems. One of the drawback of that proposal was a loss in contrast: a black pixel is translated in the reconstruction into a black region, but a white pixel is translated into a grey region (half black and half white). In this paper we propose an alternative model for reconstruction with a di erent set of operations, which we call the \Cover" semi-group. In this model we are able to obtain a better contrast than is possible in the previous one. We prove tight bounds on the contrast as a function of the complexity (number of transparencies used) of the scheme. We also show that for constructing k-out-n secret sharing schemes when n k 3 the new method is not applicable. Part of this work was done while the authors where visiting the Newton Institute, Cambridge. Part of this paper (Sections 1{3) was presented at the Cambridge Workshop on Cryptographic protocols, April 1996. y Dept. of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel. E-mail: [email protected]. Research supported by an Alon Fellowship and a grant from the Israel Science Foundation administered by the Israeli Academy of Sciences. z Dept. of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel. E-mail: [email protected].