International Association
for Cryptologic Research

Secure multiparty computation (MPC) models scenarios, where a set of mutually distrusting parties wish to compute some task over their private inputs. Assuming that the majority of the parties are honest and that the parties have access to a broadcast channel, every function can be computed with full security. Conversely, if either an honest majority or a broadcast channel cannot be assumed (as is the case in various real-world settings), then there are functionalities that cannot be computed with full security. Understanding the exact power of each of these assumptions is a valuable goal. In this paper, we study full security for solitary output functionalities (where only a single party receives an output). We focus on three-party functionalities in the point-to-point model (without broadcast), assuming an honest majority. We develop new techniques for analyzing the security of MPC protocols in the point-to-point model. Using these techniques, we are able to give a characterization for several interesting classes of solitary output three-party functionalities (including Boolean and ternary-output functionalities over a polynomial-size domain) that are computable with full security in the setting of an honest majority without a broadcast channel. Furthermore, using our techniques, we make progress in understanding the set of solitary output three-party functionalities that can be computed with full security, assuming broadcast but no honest majority. Specifically, we extend the set of such functionalities that are known to be computable, due to Halevi et al. [TCC ’19].