Protocols for Maliciously Secure Multiparty Computation with an Honest Majority in Heterogeneous Network Settings

In this work, we present novel protocols over rings for semi-honest secure three-party and malicious four-party computation with one corruption. Our protocols are optimized for heterogeneous network settings. $P_1$ and $P_2$ do not need to communicate with each other, while $P_1$ and $P_3$ communicate only in the offline phase in a single communication round. Our four-party protocol additionally requires $P_4$ to only communicate with $P_1$ in the offline phase in a single communication round. Thus, only $P_2$ and $P_3$ need to share a low latency, high bandwidth channel to achieve fast runtimes. We list several applications where this property can be useful. For instance, if $P_1$ and $P_2$ want to perform a two-party computation but share a weak network link they can utilize an auxiliary $P_3$ with a strong network link to $P_2$ to accelerate the secure computation. Our three-party protocol requires 1 domain element of global communication in the offline phase and 2 elements of global communication in the online phase. Our four-party protocol requires 2 elements of global communication in the offline phase and 3 elements of global communication in the online phase. This protocol can provide fairness and guaranteed output delivery. The best previous four-party malicious protocols with one corruption require 6 elements of global communication. We also show different ways of how to transform our protocols into homogeneous protocols where parties communicate equally on all links at the same global communication complexity.