Paper 2025/522

New Techniques for Analyzing Fully Secure Protocols: A Case Study of Solitary Output Secure Computation

Abstract

Solitary output secure computation allows a set of mutually distrustful parties to compute a function of their inputs such that only a designated party obtains the output. Such computations should satisfy various security properties such as correctness, privacy, independence of inputs, and even guaranteed output delivery. We are interested in full security, which captures all of these properties. Solitary output secure computation has been the study of many papers in recent years, as it captures many real-world scenarios. A systematic study of fully secure solitary output computation was initiated by Halevi et al. [TCC 2019]. They showed several positive and negative results, however, they did not characterize what functions can be computed with full security. Alon et al. [EUROCRYPT 2024] considered the special, yet important case, of three parties with Boolean output, where the output-receiving party has no input. They completely characterized the set of such functionalities that can be computed with full security. Interestingly, they also showed a possible connection with the seemingly unrelated notion of fairness, where either all parties obtain the output or none of them do. We continue this line of investigation and study the set of three-party solitary output Boolean functionalities where all parties hold private inputs. Our main contribution is defining and analyzing a family of ``special-round'' protocols, which generalizes the set of previously proposed protocols. Our techniques allow us to identify which special-round protocols securely compute a given functionality (if such exists). Interestingly, our analysis can also be applied in the two-party setting (where fairness is an issue). Thus, we believe that our techniques may prove useful in additional settings and deepen our understanding of the connections between the various settings.