Secure multi-party computation (MPC) allows multiple parties, each holding private data that they are unwilling to share, to collaborate to perform computations over their data, while revealing nothing other than the result. The theory behind secure computation is already 35 years old, but in the last 15 years researchers in the field have demonstrated tremendous improvement in performance. Today, a confluence of factors are driving an increased interest in secure computation, both in the public domain and in industry, including the advancements in MPC mentioned above, the explosion in the volume of private user data being generated, and the advancements in machine learning that are being deployed to leverage that private data.

In this talk, I will give an overview of several of my recent results that has helped scale the performance of secure computation. In the first half of the talk, I will focus on the setting where we have large volumes of data and a secure computation that is out-source to a small number of servers — the Few-PC setting. I will focus on a security relaxation that allows us to improve communication costs asymptotically and concretely for a large class of computations. In the second half of the talk, I will describe several results that allow us to scale MPC to thousands or even millions of parties, by demonstrating a protocol that requires less communication and computation from each participant as the number of participants grows.