Fairness versus guaranteed output delivery in secure multiparty computation

In the setting of secure multiparty computation, a set of parties wish to compute a joint function of their private inputs. The computation should preserve security properties such as privacy, correctness, independence of inputs, fairness and guaranteed output delivery. In the case of no honest majority, fairness and guaranteed output delivery cannot always be obtained. Thus, protocols for secure multiparty computation are typically of two disparate types: protocols that assume an honest majority (and achieve all properties including fairness and guaranteed output delivery), and protocols that do not assume an honest majority (and achieve all properties except for fairness and guaranteed output delivery). In addition, in the two-party case, fairness and guaranteed output delivery are equivalent. As a result, the properties of fairness (which means that if corrupted parties receive output then so do the honest parties) and guaranteed output delivery (which means that corrupted parties cannot prevent the honest parties from receiving output in any case) have typically been considered to be the same. In this paper, we initiate a study of the relation between fairness and guaranteed output delivery in secure multiparty computation. We show that in the multiparty setting these properties are distinct and proceed to study under what conditions fairness implies guaranteed output delivery (the opposite direction always holds). We also show the existence of non-trivial functions for which complete fairness is achievable (without an honest majority) but guaranteed output delivery is not, and the existence of non-trivial functions for which complete fairness and guaranteed output delivery are achievable. Our study sheds light on the role of broadcast in fairness and guaranteed output delivery, and shows that these properties should sometimes be considered separately.