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On the Exact Round Complexity of Secure Three-Party Computation

Patra, A and Ravi, D (2021) On the Exact Round Complexity of Secure Three-Party Computation. In: Journal of Cryptology, 34 (4).

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Official URL: https://doi.org/10.1007/s00145-021-09404-0


We settle the exact round complexity of three-party computation (3PC) in honest-majority setting, for a range of security notions such as selective abort, unanimous abort, fairness and guaranteed output delivery. It is a folklore that the implication holds from the guaranteed output delivery to fairness to unanimous abort to selective abort. We focus on computational security and consider two network settings�pairwise-private channels without and with a broadcast channel. In the minimal setting of pairwise-private channels, 3PC with selective abort is known to be feasible in just two rounds, while guaranteed output delivery is infeasible to achieve irrespective of the number of rounds. Settling the quest for exact round complexity of 3PC in this setting, we show that three rounds are necessary and sufficient for unanimous abort and fairness. Extending our study to the setting with an additional broadcast channel, we show that while unanimous abort is achievable in just two rounds, three rounds are necessary and sufficient for fairness and guaranteed output delivery. Our lower bound results extend for any number of parties in honest majority setting and imply tightness of several known constructions. While our lower bounds extend to the common reference string (CRS) model, all our upper bounds are in the plain model. The fundamental concept of garbled circuits underlies all our upper bounds. Concretely, our constructions involve transmitting and evaluating only constant number of garbled circuits. Assumption-wise, our constructions rely on injective (one-to-one) one-way functions. © 2021, International Association for Cryptologic Research.

Item Type: Journal Article
Publication: Journal of Cryptology
Publisher: Springer
Additional Information: The copyright for this article belongs to Springer
Keywords: Broadcasting, Broadcast channels; Common reference string models; Computational security; Fundamental concepts; Garbled circuits; Network settings; One-way functions; Private channels, Complex networks
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 24 Sep 2021 07:57
Last Modified: 24 Sep 2021 07:57
URI: http://eprints.iisc.ac.in/id/eprint/69746

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