Perfectly-Secure Synchronous MPC with Asynchronous Fallback Guarantees
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Secure multi-party computation (MPC) is a fundamental problem in secure distributed computing. The optimal resilience for perfectly-secure MPC in synchronous and asynchronous networks is t < n/3 and t < n/4 respectively, where n is the number of parties and t is the number of corruptions. A natural question is whether there exists a protocol tolerating t_s < n/3 corruptions in a synchronous network and t_a < n/4 corruptions in an asynchronous network. We design such a protocol, if 3t_s + t_a < n. For our protocol, we present a perfectly-secure Byzantine agreement (BA) protocol, tolerating t < n/3 corruptions in any network and a perfectly-secure verifiable secret-sharing (VSS) protocol, tolerating t_s and t_a corruptions in a synchronous and an asynchronous network respectively.
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