Round-efficient concurrently composable secure computation via a robust extraction lemma

We consider the problem of constructing protocols for secure computation that achieve strong concurrent and composable notions of security in the plain model. Unfortunately UC-secure secure computation protocols are impossible in this setting, but the Angel-Based Composable Security notion offers a promising alternative. Until now, however, under standard (polynomial-time) assumptions, only protocols with polynomially many rounds were known to exist. In this work, we give the first Õ (log n)-round secure computation protocol in the plain model that achieves angel-based composable security in the concurrent setting, under standard assumptions. We do so by constructing the first Õ (log n)-round CCA-secure commitment protocol. Our CCA-secure commitment protocol is secure based on the minimal assumption that one-way functions exist. A central tool in obtaining our result is a new robust concurrent extraction lemma that we introduce and prove, based on the minimal assumptions that one-way functions exist. This robust concurrent extraction lemma shows how to build concurrent extraction procedures that work even in the context of an “external” protocol that cannot be rewound by the extractor. We believe this lemma can be used to simplify many existing works on concurrent security, and is of independent interest. In fact, our lemma when used in conjunction with the concurrentsimulation schedule of Pass and Venkitasubramaniam (TCC’08), also yields a constant round construction based additionally on the existence of quasi-polynomial time (PQT) secure one-way functions.