Efficient constant round multi-party computation combining BMR and SPDZ

Recently, there has been huge progress in the field of concretely efficient secure computation, even while providing security in the presence of malicious adversaries. This is especially the case in the two party setting, where constant-round protocols exist that remain fast even over slow networks. However, in the multi-party setting, all concretely efficient fully-secure protocols, such as SPDZ, require many rounds of communication. In this paper, we present an MPC protocol that is fully-secure in the presence of malicious adversaries and for any number of corrupted parties. Our construction is based on the constant-round BMR protocol of Beaver et al., and is the first fully-secure version of that protocol that makes black-box usage of the underlying primitives, and is therefore concretely efficient. Our protocol includes an online phase that is extremely fast and mainly consists of each party locally evaluating a garbled circuit. For the offline phase we present both a generic construction (using any underlying MPC protocol), and a highly efficient instantiation based on the SPDZ protocol. Our estimates show the protocol to be considerably more efficient than previous fully-secure multi-party protocols.