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Efficient, Actively Secure MPC with a Dishonest Majority: A Survey

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Arithmetic of Finite Fields (WAIFI 2020)

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Abstract

The last ten years have seen a tremendous growth in the interest and practicality of secure multiparty computation (MPC) and its possible applications. Secure MPC is indeed a very hot research topic and recent advances in the field have already been translated into commercial products world-wide. A major pillar in this advance has been in the case of active security with a dishonest majority, mainly due to the SPDZ-line of work protocols. This survey gives an overview of these protocols, with a focus of the original SPDZ paper (Damgård et al. CRYPTO 2012) and its subsequent optimizations.

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Notes

  1. 1.

    OT is a fundamental cryptographic primitive [63, 69]. In its classical formulation, a (one-out-of-two) oblivious transfer is a two-party protocol between a sender \(P_S\) and a receiver \(P_R\): \(P_S\) inputs two messages \(x_0,x_1\), \(P_R\) inputs a bit b, and the goal is for the receiver to learn \(x_b\) and nothing more, whilst the sender learns no information about b.

  2. 2.

    Given a set S, a positive polynomial on S is such that \(p(x)>0\) for every \(x \in S\).

  3. 3.

    Roughly, the LPN assumption says that given a random linear code C, a noisy random codeword of C is pseudo-random.

  4. 4.

    This generalisation of oblivious transfer is also referred to as oblivious linear function evaluation (OLE) [57].

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Acknowledgements

I would like to thank the organizers of WAIFI 2020 for inviting me to give a talk there. I am also grateful to Axel Mertens and Nigel Smart for helpful comments. This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT and by the FWO under an Odysseus project GOH9718N.

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Orsini, E. (2021). Efficient, Actively Secure MPC with a Dishonest Majority: A Survey. In: Bajard, J.C., Topuzoğlu, A. (eds) Arithmetic of Finite Fields. WAIFI 2020. Lecture Notes in Computer Science(), vol 12542. Springer, Cham. https://doi.org/10.1007/978-3-030-68869-1_3

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