Abstract
Secure multiparty computation protocols with dynamic parties, which assume that honest parties do not need to be online throughout the whole execution of the protocol, have recently gained a lot of traction for computations of large scale distributed protocols, such as blockchains. More specifically, in Fluid MPC, introduced in (Choudhuri et al. CRYPTO 2021), parties can dynamically join and leave the computation from round to round. The best known Fluid MPC protocol in the honest majority setting communicates \(O(n^2)\) elements per gate where n is the number of parties online at a time. While Le Mans (Rachuri and Scholl, CRYPTO 2022) extends Fluid MPC to the dishonest majority setting with preprocessing, it still communicates \(O(n^2)\) elements per gate.
In this work we present alternative Fluid MPC solutions that require O(n) communication per gate for both the information-theoretic honest majority setting and the information-theoretic dishonest majority setting with preprocessing. Our solutions also achieve maximal fluidity where parties only need to be online for a single communication round. Additionally, we show that a protocol in the information-theoretic dishonest majority setting with sub-quadratic \(o(n^2)\) overhead per gate requires for each of the N parties who may ever participate in the (later) execution phase, \(\varOmega (N)\) preprocessed data per gate.
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Notes
- 1.
- 2.
We remark however that, even in [25], the preprocessing per party grows as \(\varOmega (N)\), even when quadratic communication is achieved. This preprocessing is of a different nature though and is not related to resharing, as it comes in the form of pairwise products that are used to build multiplication triples once the exact committees are known. Our result implies that, even if multiplication triples are pre-distributed within each committee, transferring the state from one committee to the next will still require \(\varOmega (N)\) preprocessing, unless \(O(n^2)\) communication is allowed. We discuss this in more detail in Sect. 5.
- 3.
Recall that a requirement in the fluid preprocessing model is that the correlations the parties receive have to be agnostic to the specific committee assignments. It may not be clear now, but it turns out multiplication triples are committee-agnostic, if the parties start with BeDOZa-style correlations [4]. This will be made clearer.
- 4.
This form of preprocessing is not committee-agnostic, but a simpler form of it is, and the actual tuple required is obtained by adding an extra resharing step. This is not relevant for our discussion.
- 5.
This kind of triple authenticated under the MAC keys of both committees \(\mathcal {C}_{i-2}\) and \(\mathcal {C}_{i-1}\) can indeed still be computed from our actual committee-agnostic preprocessing.
- 6.
[25] uses ‘l’ instead of our ‘v’ here.
- 7.
As we elaborate on below, this type of preprocessing can in fact be generated “on the fly” by the different committees, so it is not considered preprocessing as such.
- 8.
All-but-one client could be corrupted, however.
- 9.
Note that the invocations of \(\pi _{\mathsf {{MAC\text {-}check\text {-}hm}}}\) in the Check State phase of \(\pi _{\mathsf {mult\text {-}verify\text {-}hm}}\) can be condensed to 3 rounds, since only one value at a time is opened.
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Bienstock, A., Escudero, D., Polychroniadou, A. (2023). On Linear Communication Complexity for (Maximally) Fluid MPC. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14081. Springer, Cham. https://doi.org/10.1007/978-3-031-38557-5_9
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