Constant-Round MPC with Fairness and Guarantee of Output Delivery

We study the round complexity of multiparty computation with fairness and guaranteed output delivery, assuming existence of an honest majority. We demonstrate a new lower bound and a matching upper bound. Our lower bound rules out any two-round fair protocols in the standalone model, even when the parties are given access to a common reference string (CRS). The lower bound follows by a reduction to the impossibility result of virtual black box obfuscation of arbitrary circuits. Then we demonstrate a three-round protocol with guarantee of output delivery, which in general is harder than achieving fairness (since the latter allows the adversary to force a fair abort). We develop a new construction of a threshold fully homomorphic encryption scheme, with a new property that we call ``flexible\u27\u27 ciphertexts. Roughly, our threshold encryption scheme allows parties to adapt flexible ciphertexts to the public keys of the non-aborting parties, which provides a way of handling aborts without adding any communication