Improved Black-Box Constructions of Composable Secure Computation

We close the gap between black-box and non-black-box constructions of composable secure multiparty computation in the plain model under the minimal assumption of semi-honest oblivious transfer. The notion of protocol composition we target is angel-based security, or more precisely, security with super-polynomial helpers. In this notion, both the simulator and the adversary are given access to an oracle called an angel that can perform some predefined super-polynomial time task. Angel-based security maintains the attractive properties of the universal composition framework while providing meaningful security guarantees in complex environments without having to trust anyone. Angel-based security can be achieved using non-black-box constructions in max(R_OT,Õ(log n)) rounds where R_OT is the round-complexity of semi-honest oblivious transfer. However, current best known black-box constructions under the same assumption require max(R_OT,Õ(log² n)) rounds. If R_OT is a constant, the gap between non-black-box and black-box constructions can be a multiplicative factor log n. We close this gap by presenting a max(R_OT,Õ(log n)) round black-box construction. We achieve this result by constructing constant-round 1-1 CCA-secure commitments assuming only black-box access to one-way functions.