We present a round-efficient black-box construction of a general multi-party computation (MPC) protocol that satisfies composability in the plain model. The security of our protocol is proven in the angel-based UC framework [Prabhakaran and Sahai, STOC’04] under the minimal assumption of the existence of semi-honest oblivious transfer protocols. The round complexity of our protocol is $$\max (\widetilde{O}(\log ^2n), O(R_{{{{\mathsf {O}}}{{\mathsf {T}}}}}))$$ when the round complexity of the underlying oblivious transfer protocol is $$R_{{{{\mathsf {O}}}{{\mathsf {T}}}}}$$ . Since constant-round semi-honest oblivious transfer protocols can be constructed under standard assumptions (such as the existence of enhanced trapdoor permutations), our result gives a $$\widetilde{O}(\log ^2n)$$ -round protocol under these assumptions. Previously, only an $$O(\max (n^{\epsilon }, R_{{{{\mathsf {O}}}{{\mathsf {T}}}}}))$$ -round protocol was shown, where $$\epsilon >0$$ is an arbitrary constant. We obtain our MPC protocol by constructing a $$\widetilde{O}(\log ^2n)$$ -round CCA-secure commitment scheme in a black-box way under the assumption of the existence of one-way functions.