International Association for Cryptologic Research

International Association
for Cryptologic Research


On the Power of an Honest Majority in Three-Party Computation Without Broadcast

Bar Alon
Ran Cohen
Eran Omri
Tom Suad
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Presentation: Slides
Abstract: Fully secure multiparty computation (MPC) allows a set of parties to compute some function of their inputs, while guaranteeing correctness, privacy, fairness, and output delivery. Understanding the necessary and sufficient assumptions that allow for fully secure MPC is an important goal. Cleve (STOC'86) showed that full security cannot be obtained in general without an honest majority. Conversely, by Rabin and Ben-Or (FOCS'89), assuming a broadcast channel and an honest majority, any function can be computed with full security. Our goal is to characterize the set of functionalities that can be computed with full security, assuming an honest majority, but no broadcast. This question was fully answered by Cohen et al. (TCC'16) -- for the restricted class of \emph{symmetric} functionalities (where all parties receive the same output). Instructively, their results crucially rely on \emph{agreement} and do not carry over to general \emph{asymmetric} functionalities. In this work, we focus on the case of three-party asymmetric functionalities, providing a variety of necessary and sufficient conditions to enable fully secure computation. An interesting use-case of our results is \emph{server-aided} computation, where an untrusted server helps two parties to carry out their computation. We show that without a broadcast assumption, the resource of an external non-colluding server provides no additional power. Namely, a functionality can be computed with the help of the server if and only if it can be computed without it. For fair coin tossing, we further show that the optimal bias for three-party (server-aided) $r$-round protocol remains $\Theta(1/r)$ (as in the two-party setting).
Video from TCC 2020
  title={On the Power of an Honest Majority in Three-Party Computation Without Broadcast},
  booktitle={Theory of Cryptography},
  author={Bar Alon and Ran Cohen and Eran Omri and Tom Suad},