Efficient Mixed-Protocol Secure Four-Party Computation with Private Robustness

Secure honest-majority four-party computation (4PC) protocol was proposed for four mutually-distrusting parties to jointly evaluate a complex function on their private inputs with private robustness by cheater identification. This capability has great potential for distributed private computation, such as distributed privacy-preserving machine learning. However, the adoption of secure 4PC is hampered mainly by the computation and communication costs of online phase of protocol. In this work we propose an efficient secure 4PC protocol with private robustness. Specifically, by transferring hash verification operation for cheating detection to the fourth party, and with the help of the mutual constraint between the four parties, the communication rounds and communication costs of joint message passing primitive can be reduced. To further reduce communication cost, this paper proposes to divide the four parties into two groups and applies the method of two-party multiplication with truncation to avoid multiplication overflow. We implement secure 4PC protocol and demonstrate the efficiency of computation and communication in MNIST multi-class classification training. It achieves$2.1\times$reduction in computation cost and$2.5\times$reduction in communication cost compared to prior works.