Completely fair SFE and coalition-safe cheap talk

Secure function evaluation (SFE) enables a group of players, by themselves, to evaluate a function on private inputs as securely as if a trusted third party had done it for them. A completely fair SFE is a protocol in which, conceptually, the function values are learned atomically.We provide a completely fair SFE protocol which is secure for any number of malicious players, using a novel combination of computational and physical channel assumptions.We also show how completely fair SFE has striking applications togame theory. In particular, it enables "cheap-talk" protocol that(a) achieve correlated-equilibrium payoffs in any game, (b) are the first protocols which provably give no additional power to any coalition of players, and (c) are exponentially more efficient than prior counterparts.