3-out-of-n cheating prevention visual cryptographic schemes

In literature, (2, n) cheating prevention visual cryptographic schemes (CPVCSs) have been proposed, dealing with the case of dishonest participants, called cheaters, who can collude together to force honest participants to reconstruct a wrong secret. While (2, n)-CPVCSs resistant to deterministic cheating have been presented, the problem of defining (k, n)-CPVCS for any k has not been solved. In this paper, we discub (3, n)-CPVCS, and propose three (3, n)-CPVCSs with different cheating prevention capabilities. To show the effectiveneb of the presented (3, n)-CPVCS, some experimental results are discubed as well.