  We describe scalable protocols for solving the secure multi-party computation
(MPC) problem among a large 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 setting, 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 field
elements and perform an amount of computation that is $\tilde{O}(m/n + \sqrt
n)$. We also show that our protocols provide perfect and universally-composable
security.
  To achieve our asynchronous MPC result, we define the \emph{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.
