A secure multi-party computation (MPC) protocol enables mutually untrusting parties to jointly evaluate a function f over their private inputs, while guaranteeing that information on their inputs will not be revealed beyond the function output.
We are interested in secure computation protocols in settings where the number of parties is huge, and their data even larger. In this regime, the efficiency of existing solutions breaks down: either requiring resources linear in the circuit representation size of the function, or requiring parties to store and communicate information on the order of all parties' combined inputs.
Assuming the existence of a single-use broadcast channel (per player), we demonstrate statistically secure n-party computation protocols for computing (multiple) arbitrary dynamic RAM programs over parties’ inputs, handling (1/3−ε) fraction static corruptions, while preserving up to polylogarithmic factors the computation and memory complexities of the RAM program. Additionally, our protocol is load balanced across all parties, and achieves polylogarithmic communication locality (i.e., each party only ever needs to speak to polylog(n) other parties).