A Unified Framework for UC from Only OT

In [1], the authors presented a unified framework for constructing Universally Composable (UC) secure computation protocols, assuming only enhanced trapdoor permutations. In this work, we weaken the hardness assumption underlying the unified framework to only the existence of a stand-alone secure semi-honest Oblivious Transfer (OT) protocol. The new framwork directly implies new and improved UC feasibility results from only the existence of a semi-honest OT protocol in various models. Since in many models, the existence of UC-OT implies the existence of a semi-honest OT protocol. Furthermore, we show that by relying on a more fine-grained analysis of the unified framework, we obtain concurrently secure computation protocols with super-polynomial-time simulation (SPS), based on the necessary assumption of the existence of a semi-honest OT protocol that can be simulated in super-polynomial times. When the underlying OT protocol has constant rounds, the SPS secure protocols constructed also have constant rounds. This yields the first construction of constant-round secure computation protocols that satisfy a meaningful notions of concurrent security (i.e., SPS security) based on tight assumptions. A notable corollary following from our new unifed framwork is that standalone (or bounded-concurrent) password authenticated key-exchange protocols (PAKE) can be constructed from only semi-honest OT protocols; combined with the result of [2] that the existence of PAKE protocols implies that of OT, we derive a tight characterization of PAKE protocols.