Perfectly-Secure Synchronous MPC With Asynchronous Fallback Guarantees

Secure multi-party computation (MPC) is a fundamental problem in secure distributed computing. An MPC protocol allows a set of $n$ mutually distrusting parties to carry out any joint computation of their private inputs, without disclosing any additional information about their inputs. MPC with information-theoretic security (also called unconditional security) provides the strongest security guarantees and remains secure even against computationally unbounded adversaries. Perfectly-secure MPC protocols are a class of information-theoretically secure MPC protocols, which provide all the security guarantees in an error-free fashion. The focus of this work is perfectly-secure MPC. Known protocols are designed assuming either a synchronous or asynchronous communication network. It is well known that perfectly-secure synchronous MPC is possible as long as the adversary can corrupt any $t_{s} < n/3$ parties. On the other hand, perfectly-secure asynchronous MPC protocols can tolerate up to $t_{a} < n/4$ corrupt parties. A natural question is does there exist a single MPC protocol for the setting where the parties are not aware of the exact network type and which can tolerate up to $t_{s} < n/3$ corruptions in a synchronous network and up to $t_{a} < n/4$ corruptions in an asynchronous network. We design such a best-of-both-worlds perfectly-secure MPC protocol, provided $3t_{s} + t_{a} < n$ holds. For designing our protocol, we design two important building blocks which are of independent interest. The first building block is a best-of-both-worlds Byzantine agreement (BA) protocol tolerating $t < n/3$ corruptions which remains secure both in a synchronous as well as asynchronous network. The second building block is a polynomial-based best-of-both-worlds verifiable secret-sharing (VSS) protocol, which can tolerate up to $t_{s}$ and $t_{a}$ corruptions in a synchronous and in an asynchronous network respectively.