Almost-Asynchronous MPC with Faulty Minority.
Zuzana Beerliová-Trubíniová, Martin Hirt, Jesper Buus Nielsen · 2008
Abstract. Secure multiparty computation (MPC) allows a set of parties to securely evaluate any agreed function of their inputs, even when up to t of the n parties are faulty. Protocols for synchronous networks (where every sent message is assumed to arrive within a constant time) tolerate up to t < n/2 faulty parties, whereas in the more realistic asynchronous setting (with no a priory information on maximal message delay) only security against t < n/3 is possible. Note that even asynchronous Byzantine agreement requires t < n/3. In this paper, we are interested in the minimal synchronicity assumption for achieving security against t < n/2. It turns out that the bottleneck of asynchronous MPC is the distribution of the inputs: Once the inputs are correctly distributed, any deterministic function can be computed over a fully asynchronous network with t < n/2. Furthermore, we show that the inputs can be verifiably distributed with t < n/2, if a single round of synchronous broadcast is available. Composing the above, we obtain the first MPC protocol that achieves security against t < n/2 without assuming a fully synchronous network. Actually our protocol guarantees security against any faulty minority in an almost asynchronous network, i.e. in a network with one single round of synchronous broadcast (followed by a fully asynchronous communication). Furthermore our protocol takes inputs of all parties (in a fully asynchronous network only inputs of n−t parties can be guaranteed), and so achieves everything that is possible in synchronous networks (but impossible in fully asynchronous networks) at the price of just one synchronous broadcast round. As tools for our protocol we introduce the notions of almost non-interactive verifiable secret-sharing and almost non-interactive zero-knowledge proof of knowledge, which are of independent interest as they can serve as efficient replacements for fully non-interactive verifiable secret-sharing and fully non-interactive zero-knowledge proof of knowledge.