Fully homomorphic encryption reduces the communication necessary for MPC to a minimum. Since FHE is, at the moment, way too slow to be useful, work has gone in

Fully homomorphic encryption reduces the communication necessary for MPC to a minimum. Since FHE is, at the moment, way too slow to be useful, work has gone in the direction of mixing classic techniques with somewhat homomorphic encryption, cf. http://eprint.iacr.org/2010/514 http://eprint.iacr.org/2010/514 http://eprint.iacr.org/2011/535 http://eprint.iacr.org/2011/535 http://eprint.iacr.org/2011/663 http://eprint.iacr.org/2011/663