Alex will present a recent result submitted to Eurocrypt; abstract below.

Motivated by the fact that the only real-world deployments of multi-party computation are for a small number of parties, we investigate efficient secure-computation protocols for the particular case of three parties. Combining various two-party techniques (such as cut-and-choose and oblivious authenticated bits) with the idea of player simulation, we construct a constant-round three-party protocol, tolerating any number of malicious, corrupted parties, which has significantly better efficiency than prior work.  Our techniques also give an efficient constant-round two-party protocol with malicious security, requiring only a single garbled circuit to be generated and uses significantly less online communication and computation than existing constant-round protocols.