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

Patra, A and Ravi, D (2023) Beyond Honest Majority: The Round Complexity of Fair and Robust Multi-party Computation. In: Journal of Cryptology, 36 (3).

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Abstract

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 generalized 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 ta+ tp< n , where ta, tp 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 (ta, tp) starting from (⌈n2⌉-1,⌊n2⌋) to (0 , n- 1) , the boundary corruption restricts the adversary only to the boundary cases of (⌈n2⌉-1,⌊n2⌋) 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 ⌈n2⌉-1 . We target the round complexity of fair and robust MPC tolerating dynamic and boundary adversaries. As it turns out, ⌈n2⌉+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 pairwise-private and broadcast channels and hold in the presence of correlated randomness setup (which subsumes 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 and GOD protocols.

Item Type:	Journal Article
Publication:	Journal of Cryptology
Publisher:	Springer
Additional Information:	The copyright for this article belongs to the Springer.
Keywords:	Boundary; Dynamic; Fairness; Guaranteed output delivery; MPC; Round complexity
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	28 Jul 2023 08:45
Last Modified:	28 Jul 2023 08:45
URI:	https://eprints.iisc.ac.in/id/eprint/82576

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