Three Steps

摘要

Given is a deal of ten cards over three players, such that two players each get four cards and the remaining player (the 'eavesdropper') two cards. We show that there does not exist a protocol of two steps for the four-card players to inform each other safely of their hands of cards, and we then present a protocol of three steps that achieves that goal. We verify the properties of that protocol by combinatorial and, mainly, logical (model checking) means. No such three-step protocol for cards was known. The method can be generalized. This will advance the characterization of card deals for which such exchanges of secrets are possible.