Round-Preserving Parallel Composition of Probabilistic-Termination Cryptographic Protocols

An important benchmark for multi-party computation protocols (MPC) is their round complexity. For several MPC tasks, such as broadcast, (tight) lower bounds on the complexity are known. However, some of these can be circumvented when termination every party not a priori known, and simultaneous guaranteed. Protocols with this property called probabilistic-termination (PT) protocols. Running PT in parallel affects resulting protocol somewhat unexpected ways. instance, an execution m constant expected might take $$O(\log m)$$ rounds to complete. In seminal work, Ben-Or El-Yaniv (Distributed Computing ‘03) developed technique arbitrarily many broadcast protocols, while preserving More recently, Cohen et al. (CRYPTO ‘16) devised framework universal composition provided first composable parallel-broadcast simulation-based proof. These constructions crucially rely fact that “privacy-free,” do generalize arbitrary straightforward way. This raises question whether it possible execute parallel, without increasing paper we tackle provide both feasibility infeasibility results. We construct round-preserving compiler, tolerating any dishonest minority actively corrupted parties, compiles into realizing composition, having black-box access underlying Furthermore, prove same cannot achieved, using known techniques, given only functionalities realized by unless merely security against semi-honest corruptions required, which case protocol. To our results, utilize language results al., extend capture reactive functionalities, handle honest majority.