[Resource Topic] 2019/998: Beyond Honest Majority: The Round Complexity of Fair and Robust Multi-party Computation

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

Authors: Arpita Patra, Divya Ravi


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 (t_a,t_p) starting from (\lceil \frac{n}{2} \rceil - 1 , \lfloor \frac{n}{2} \rfloor) to (0,n-1), the boundary corruption restricts the adversary only to the boundary cases of (\lceil \frac{n}{2} \rceil - 1, \lfloor \frac{n}{2} \rfloor) and (0,n-1). Notably, both corruption settings empower an adversary to control majority of the parties, yet ensuring the count on active corruption never goes beyond \lceil \frac{n}{2} \rceil - 1. We target the round complexity of fair and robust MPC tolerating dynamic and boundary adversaries. As it turns out, \lceil \frac{n}{2} \rceil + 1 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 3 and 4 is necessary and sufficient for fair and GOD protocols respectively, with the latter having an exception of allowing 3 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 3 and 2 rounds in the presence of public and private setup respectively for both fair as well as GOD protocols.

ePrint: https://eprint.iacr.org/2019/998

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