Visual cryptograms of random grids for threshold access structures

Based on a new model of visual cryptograms of random grids (VCRG), we design novel algorithms to generate a set of threshold (k,n)(k,n)-VCRG for sharing a secret image P among n participants in such a way that any group of k out of the n encrypted transparencies reveals P to our eyes when superimposed, while any group of less than k transparencies obtains nothing about P  . Just like conventional visual cryptographic schemes (VCSs), our designs require none of computing devices but merely human visual ability in the decryption process. Yet, our VCRG approach is much simpler and does not need any extra pixel expansion which is inevitable (actually 1/2k−11/2k−1 for n=kn=k and even larger for n>kn>k) in VCSs. The correctness of our algorithms is formally proved and experimentally demonstrated. The light contrast in our best algorithm is cautiously analyzed and shown to be as effective as that in a quality threshold VCS when k shares are superimposed. With theoretic and practical interests, our VCRG model exposes new possibilities to the researches of visual secret sharing.