Linear Communication in Malicious Majority MPC

The SPDZ multiparty computation protocol :DPSZ12 allows n parties to securely compute arithmetic circuits over a finite field, while tolerating up to n-1 active corruptions. A line of work building upon SPDZ has made considerable improvement to the protocol's performance, typically focusing on concrete efficiency. However, the communication complexity of each of these protocols is Ømega(n^2|C|).