NANOPI: Extreme-Scale Actively-Secure Multi-Party Computation.

Existing actively-secure MPC protocols require either linear rounds or linear space. Due to this fundamental space-round dilemma, no existing MPC protocols is able to run large-scale computations without significantly sacrificing performance. To mitigate this issue, we developed nanoPI, which is practically efficient in terms of both time and space. Our protocol is based on WRK but introduces interesting and necessary modifications to address several important programmatic and cryptographic challenges. A technique that may be of independent interest (in transforming other computation-oriented cryptographic protocols) is a staged execution model, which we formally define and realize using a combination of lightweight static and dynamic program instrumentation. Our techniques are integrated in nanoPI, an open-source tool for efficiently building and running actively-secure extreme-scale MPC applications. We demonstrate the unprecedented scalability and performance of nanoPI by building and running a suit of bench- mark applications, including an actively-secure four-party logistical regression (involving 4.7 billion ANDs and 8.9 billion XORs) which finished in less than 28 hours on four small-memory machines.