Paper 2019/998

Beyond Honest Majority: The Round Complexity of Fair and Robust Multi-party Computation

Arpita Patra and Divya Ravi

Abstract

Two of the most sought-after properties of Multi-party Computation (MPC) protocols are fairness and guaranteed output delivery (GOD), the latter also referred to as robustness. Achieving both, however, brings in the necessary requirement of malicious-minority. In a generalised adversarial setting where the adversary is allowed to corrupt both actively and passively, the necessary bound for a $n$-party fair or robust protocol turns out to be $t_a+t_p<n$, where $t_a,t_p$ denote the threshold for active and passive corruption with the latter subsuming the former. Subsuming the malicious-minority as a boundary special case, this setting, denoted as dynamic corruption, opens up a range of possible corruption scenarios for the adversary. While dynamic corruption includes the entire range of thresholds for $$ starting from $$ to $$, the boundary corruption restricts the adversary only to the boundary cases of $$ and $$. Notably, both corruption settings empower an adversary to control majority of the parties, yet ensuring the count on active corruption never goes beyond $$. We target the round complexity of fair and robust MPC tolerating dynamic and boundary adversaries. As it turns out, $$ rounds are necessary and sufficient for fair as well as robust MPC tolerating dynamic corruption. The non-constant barrier raised by dynamic corruption can be sailed through for a boundary adversary. The round complexity of $$ and $$ is necessary and sufficient for fair and GOD protocols respectively, with the latter having an exception of allowing $$ round protocols in the presence of a single active corruption. While all our lower bounds assume pair-wise private and broadcast channels and are resilient to the presence of both public (CRS) and private (PKI) setup, our upper bounds are broadcast-only and assume only public setup. The traditional and popular setting of malicious-minority, being restricted compared to both dynamic and boundary setting, requires $$ and $$ rounds in the presence of public and private setup respectively for both fair as well as GOD protocols.

Note: This article is a full and extended version of an earlier article to appear ASIACRYPT 2019.