The Russian cards problem : a

Suppose we have a stack of cards that is divided over some players. It may be possible to communicate your hand of cards to another player by public announcements, without yet another player learning any of your cards. A solution to this problem consists of some sequence of announcements and is called an exchange. It is called a direct exchange if it consists of (the minimum of) two announcements only. The announcements in an exchange have a special form: they are safe communications, an interesting new form of update. Certain unsafe communications turn out to be unsuccessful updates. A communication is a public announcement that is known to be true. Each communication may be about a set of alternative card deals only, and even about a set of alternatives to the communicating player's own hand only. There are 102 direct exchanges for a deal of seven cards where the two players holding three cards communicate their hands to each other. Our work can be used to design cryptographic protocols for `perfect logicians' where secrets are not just computationally unfeasible to uncover but cannot be uncovered at all.