Secure Computation with Partial Message Loss

Existing communication models for multiparty computation (MPC) either assume that all messages are delivered eventually or any message can be lost. Under the former assumption, MPC protocols guaranteeing output delivery are known. However, this assumption may not hold in some network settings like the Internet where messages can be lost due to denial of service attack or heavy network congestion. On the other hand, the latter assumption may be too conservative. Known MPC protocols developed under this assumption have an undesirable feature: output delivery is not guaranteed even only one party suffers message loss. In this work, we propose a communication model which makes an intermediate assumption on message delivery. In our model, there is a common global clock and three types of parties: (i) Corrupted parties (ii) Honest parties with connection problems (where message delivery is never guaranteed) (iii) Honest parties that can normally communicate but may lose a small fraction of messages at each round due to transient network problems. We define secure MPC under this model. Output delivery is guaranteed to type (ii) parties that do not abort and type (iii) parties. Let n be the total number of parties, ef and ec be upper bounds on the number of corrupted parties and type (ii) parties respectively. We construct a secure MPC protocol for n > 4ef + 3ec. Protocols for broadcast and verifiable secret sharing are constructed along the way.