Abstract
In this work we present a novel actively secure dishonest majority MPC protocol, SuperPack, whose efficiency improves as the number of honest parties increases. Concretely, let \(0<\epsilon <1/2\) and consider an adversary that corrupts \(t<n(1-\epsilon )\) out of n parties. SuperPack requires \(6/\epsilon \) field elements of online communication per multiplication gate across all parties, assuming circuit-dependent preprocessing, and \(10/\epsilon \) assuming circuit-independent preprocessing. In contrast, most of previous works such as SPDZ (Damgård et al., ESORICS 2013) and its derivatives perform the same regardless of whether there is only one honest party, or a constant (non-majority) fraction of honest parties. The only exception is due to Goyal et al. (CRYPTO 2022), which achieves \(58/\epsilon + 96/\epsilon ^2\) field elements assuming circuit-independent preprocessing. Our work improves this result substantially by a factor of at least 25 in the circuit-independent preprocessing model.
Practically, we also compare our work with the best concretely efficient online protocol Turbospeedz (Ben-Efraim et al., ACNS 2019), which achieves \(2(1-\epsilon )n\) field elements per multiplication gate among all parties. Our online protocol improves over Turbospeedz as n grows, and as \(\epsilon \) approaches 1/2. For example, if there are \(90\%\) corruptions (\(\epsilon =0.1\)), with \(n=50\) our online protocol is \(1.5\times \) better than Turbospeedz and with \(n=100\) this factor is \(3\times \), but for \(70\%\) corruptions (\(\epsilon =0.3\)) with \(n=50\) our online protocol is \(3.5\times \) better, and for \(n=100\) this factor is \(7\times \).
Our circuit-dependent preprocessing can be instantiated from OLE/VOLE. The amount of OLE/VOLE correlations required in our work is a factor of \(\approx \epsilon n/2\) smaller than these required by Le Mans (Rachuri and Scholl, CRYPTO 2022) leveraged to instantiate the preprocessing of Turbospeedz.
Our dishonest majority protocol relies on packed secret-sharing and leverages ideas from the honest majority TurboPack (Escudero et al., CCS 2022) protocol to achieve concrete efficiency for any circuit topology, not only SIMD. We implement both SuperPack and Turbospeedz and verify with experimental results that our approach indeed leads to more competitive runtimes in distributed environments with a moderately large number of parties.
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Notes
- 1.
An example is [10] which achieves slightly sub-linear communication complexity in the circuit size at the cost of increasing the preprocessed data size to be quadratic in the circuit size.
- 2.
The work [22] does not analyze the concrete cost of their malicious protocol. We obtain this number by counting the amount of communication in their construction. We note that the protocol in [22] also needs to interact for addition gates. Our reported number assumes that the amount of addition gates is the same as the amount of multiplication gates.
- 3.
The only term that is related to the circuit depth is in the form of \(O(n\cdot \texttt{Depth})\). This is because of the use of packed secret sharing which requires to evaluate at least O(n) gates per layer. A similar term also occurs in previous works that use packed secret sharings [2, 11, 15, 17, 21, 22].
- 4.
In this work, we only focus on deterministic functions. A randomized function can be transformed into a deterministic function by taking as input an additional random tape from each party. The XOR of the input random tapes of all parties is used as the randomness of the randomized function.
- 5.
TurboPack is available at https://github.com/deescuderoo/turbopack.
- 6.
SuperPack is available at https://github.com/ckweng/SuperPack.
- 7.
- 8.
We implemented the online phase of Turbospeedz in our framework for a fair comparison.
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Escudero, D., Goyal, V., Polychroniadou, A., Song, Y., Weng, C. (2023). SuperPack: Dishonest Majority MPC with Constant Online Communication. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14005. Springer, Cham. https://doi.org/10.1007/978-3-031-30617-4_8
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