Secure multi-party computation in large networks

We describe scalable protocols for solving the secure multi-party computation (MPC) problem among a significant number of parties. We consider both the synchronous and the asynchronous communication models. In the synchronous setting, our protocol is secure against a static malicious adversary corrupting less than a 1/3 fraction of the parties. In the asynchronous environment, we allow the adversary to corrupt less than a 1/8 fraction of parties. For any deterministic function that can be computed by an arithmetic circuit with m gates, both of our protocols require each party to send a number of messages and perform an amount of computation that is (O) over tilde (m/n + root n). We also show that our protocols provide statistical and universally-composable security. To achieve our asynchronous MPC result, we define the threshold counting problem and present a distributed protocol to solve it in the asynchronous setting. This protocol is load balanced, with computation, communication and latency complexity of O (log n), and can also be used for designing other load-balanced applications in the asynchronous communication model.