Parallel coin-tossing and constant-round secure two-party computation

In this paper we show that any two-party functionality can be securely computed in a constant number of rounds, where security is obtained against (polynomial-time) malicious adversaries that may arbitrarily deviate from the protocol specification. This is in contrast to Yao's constant-round protocol that ensures security only in the face of semi-honest adversaries, and to its malicious adversary version that requires a polynomial number of rounds. In order to obtain our result, we present a constant-round protocol for secure coin-tossing of polynomially many coins (in parallel). We then show how this protocol can be used in conjunction with other existing constructions in order to obtain a constant-round protocol for securely computing any two-party functionality. On the subject of coin-tossing, we also present a constant-round almost perfect coin-tossing protocol, where by "almost perfect" we mean that the resulting coins are guaranteed to be statistically close to uniform (and not just pseudorandom).