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Secure Massively Parallel Computation for Dishonest Majority

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12551)

Abstract

This work concerns secure protocols in the massively parallel computation (MPC) model, which is one of the most widely-accepted models for capturing the challenges of writing protocols for the types of parallel computing clusters which have become commonplace today (MapReduce, Hadoop, Spark, etc.). Recently, the work of Chan et al. (ITCS ’20) initiated this study, giving a way to compile any MPC protocol into a secure one in the common random string model, achieving the standard secure multi-party computation definition of security with up to 1/3 of the parties being corrupt.

We are interested in achieving security for much more than 1/3 corruptions. To that end, we give two compilers for MPC protocols, which assume a simple public-key infrastructure, and achieve semi-honest security for all-but-one corruptions. Our first compiler assumes hardness of the learning-with-errors (LWE) problem, and works for any MPC protocol with “short” output—that is, where the output of the protocol can fit into the storage space of one machine, for instance protocols that output a trained machine learning model. Our second compiler works for any MPC protocol (even ones with a long output, such as sorting) but assumes, in addition to LWE, indistinguishability obfuscation and a circular secure variant of threshold FHE. Both protocols allow the attacker to choose corrupted parties based on the trusted setup, an improvement over Chan et al., whose protocol requires that the CRS is chosen independently of the attacker’s choices.

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Notes

  1. 1.

    If N is one Petabyte (\(10^6\) Gigabytes), then the storage of each machine in the cluster needs to be \(< 16\) Gigabytes.

  2. 2.

    We assume for simplicity that a data record takes up one bit.

  3. 3.

    Note that although the Shamir-based TFHE scheme in [20] requires a field size which is polynomial in the number of parties n, the field size in the simpler additive-based scheme is independent of n, which is crucial in our construction.

  4. 4.

    As noted in the technical overview, although this does not hold for the Shamir-based TFHE scheme in [20], it does hold for the simpler additive-based TFHE scheme given in the same paper.

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Acknowledgments

We would like to thank Shir Maimon and Wei-Kai Lin for helpful discussions. We gratefully acknowledge the TCC ’20 reviewers for their thoughtful comments. We would like to thank Tatsuaki Okamoto for being supportive of this work.

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Fernando, R., Komargodski, I., Liu, Y., Shi, E. (2020). Secure Massively Parallel Computation for Dishonest Majority. In: Pass, R., Pietrzak, K. (eds) Theory of Cryptography. TCC 2020. Lecture Notes in Computer Science(), vol 12551. Springer, Cham. https://doi.org/10.1007/978-3-030-64378-2_14

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