Collusion-free protocols

Secure protocols attempt to minimize the injuries to privacy and correctness inflicted by malicious participants who collude during run-time. They do not, however, prevent malicious parties from colluding and coordinating their actions in the first place!Eliminating such collusion of malicious parties during the execution of a protocol is an important and exciting direction for research in Cryptography. We contribute the first general result in this direction: (1) We provide a rigorous definition of what a collusion-free protocol is; and (2) We prove that, under standard physical and computational assumptions ---i.e., plain envelopes and trapdoor permutations---collusion-free protocols exist for all finite protocol tasks with publicly observable actions. (Note that such tasks are allowed to have secret global state, and thus include Poker, Bridge, and other such games.Our solution is tight in the sense that, for a collusion-free protocol to exist, each of (a) the finiteness of the game of interest, (b) the public observability of its actions, and (c) the use of some type of physically private channel is provably essential.