Universally Composable Almost-Everywhere Secure Computation

Most existing work on secure multi-party computation (MPC) ignores a key idiosyncrasy of modern communication networks, that there are a limited number of communication paths between any two nodes, many of whom might even be corrupted. The work by Garay and Ostrovsky [EUROCRYPT’08] on almost-everywhere MPC (AE-MPC), introduced “best-possible security” properties for MPC over such incomplete networks, where necessarily some of the honest parties may be excluded from the computation—we call such parties “doomed.” In this work we provide a universally composable definition of almost-everywhere security, which allows us to automatically and accurately capture the guarantees of AE-MPC (as well as AE-communication, the analogous “best-possible security” version of secure communication) in the Universal Composability (UC) framework of Canetti. Our result offers the first simulation-based treatment of this important but under-investigated problem, along with the first simulation-based proof of AE-MPC.