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In this work, we study the intrinsic complexity of black-box Universally Composable UC secure computation based on general assumptions. We present a thorough study in various corruption modelings while focusing on achieving security in the common reference string CRS model. Our results involve the following:Static UC Secure Computation. Designing the first static UC secure oblivious transfer protocol based on public-key encryption and stand-alone semi-honest oblivious transfer. As a corollary we obtain the first black-box constructions of UC secure computation assuming only two-round semi-honest oblivious transfer.One-sided UC Secure Computation. Designing adaptive UC secure two-party computation with single corruptions assuming public-key encryption with oblivious ciphertext generation.Adaptive UC Secure Computation. Designing adaptively secure UC commitment scheme assuming only public-key encryption with oblivious ciphertext generation. As a corollary we obtain the first black-box constructions of adaptive UC secure computation assuming only trapdoor simulatable public-key encryption as well as a variety of concrete assumptions.We remark that such a result was not known even under non-black-box constructions.

On Black-Box Complexity of Universally Composable Security in the CRS Model