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TurboPack: Honest Majority MPC with Constant Online Communication
Authors: Daniel Escudero, Vipul Goyal, Antigoni Polychroniadou, Yifan SongAbstract:
We present a novel approach to honest majority secure multiparty computation in the preprocessing model with information theoretic security that achieves the best online communication complexity. The online phase of our protocol requires 12 elements in total per multiplication gate with circuit-dependent preprocessing, or 20 elements in total with circuit-independent preprocessing. Prior works achieved linear online communication complexity in n, the number of parties, with the best prior existing solution involving 1.5n elements per multiplication gate. Only one recent work (Goyal et al, CRYPTO’22) achieves constant online communication complexity, but the constants are large (108 elements for passive security, and twice that for active security). That said, our protocol offers a very efficient information theoretic online phase for any number of parties.
The total end-to-end communication cost with the preprocessing phase is linear in n, i.e., 10n + 44, which is larger than the 4n complexity of the state-of-the-art protocols. The gap is not significant when the online phase must be optimized as a priority and a reasonably large number of parties is involved. Unlike previous works based on packed secret-sharing to reduce communication complexity, we further reduce the communication by avoiding the use of complex and expensive network routing or permutations tools. Furthermore, we also allow for a maximal honest majority adversary, while most previous works require the set of honest parties to be strictly larger than a majority.
Our protocol is simple and offers concrete efficiency. To illustrate this we present a full-fledged implementation together with experimental results that show improvements in online phase runtimes that go up to 5\times in certain settings (e.g. 45 parties, LAN network, circuit of depth 10 with $1$M gates).
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