Multiparty Secret Key Exchange Using a Random Deal of Cards

We consider the problem of multiparty secret key exchange. A “team” of players P₁ through P_k wishes to determine an n-bit secret key in the presence of a computationally unlimited eavesdropper, Eve. The team players are dealt hands of cards of prespecified sizes from a deck of d distinct cards; any remaining cards are dealt to Eve. We explore how the team can use the information contained in their hands of cards to determine an n-bit key that is secret from Eve, that is, an n bit string which each team player knows exactly but for which Eve’s probability of guessing the key correctly is 1/2n both before and after she hears the communication between the team players. We describe randomized protocols for secret key exchange that work for certain classes of deals, and we present some conditions on the deal for such a protocol to exist.