Round-Efficient Black-Box Construction of Composable Multi-Party Computation

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 (O(log ^2n), O(R_𝖮𝖳)) when the round complexity of the underlying oblivious transfer protocol is R_𝖮𝖳 . 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 O(log ^2n) -round protocol under these assumptions. Previously, only an O(max (n^ϵ, R_𝖮𝖳)) -round protocol was shown, where ϵ >0 is an arbitrary constant. We obtain our MPC protocol by constructing a O(log ^2n) -round CCA-secure commitment scheme in a black-box way under the assumption of the existence of one-way functions.