Secure Multi-Party Computation in Large Networks

TL;DR

This paper introduces scalable secure multi-party computation protocols for large networks, achieving security against malicious adversaries in both synchronous and asynchronous models with efficient communication and computation.

Contribution

It presents novel protocols for MPC in large networks, including solutions for asynchronous settings and the threshold counting problem, with universal security guarantees.

Findings

Protocols are secure against less than 1/3 and 1/8 adversaries in synchronous and asynchronous models.

Communication and computation complexity is approximately ore(m/n + \u007Esqrt n) for each party.

The asynchronous protocol for threshold counting is load balanced with O(log n) complexity.

Abstract

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.