Abstract
We show that the recent, highly efficient, three-party honest-majority computationally-secure MPC protocol of Araki et al. can be generalised to an arbitrary \(Q_2\) access structure. Part of the performance of the Araki et al. protocol is from the fact it does not use a complete communication network for the most costly part of the computation. Our generalisation also preserves this property. We present both passively- and actively-secure (with abort) variants of our protocol. In all cases we require fewer communication channels for secure multiplication than Maurer’s “MPC-Made-Simple” protocol for \(Q_2\) structures, at the expense of requiring pre-shared secret keys for Pseudo-Random Functions.
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Notes
- 1.
See https://homes.esat.kuleuven.be/~nsmart/SCALE/ for details.
- 2.
Note, as is common in security systems we assume channels are uni-directional; as good security practice is to have different secret keys securing communication in different directions so as to avoid various reflection attacks etc. This is exactly how TLS and IPSec secure channels are configured.
- 3.
The alterations to the protocol for when there is no surjective partition are discussed in Sect. 4.
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Acknowledgements
This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contract No. N66001-15-C-4070, and by EPSRC via grants EP/M012824 and EP/N021940/1.
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Keller, M., Rotaru, D., Smart, N.P., Wood, T. (2018). Reducing Communication Channels in MPC. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_10
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