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Maliciously Secure Massively Parallel Computation for All-but-One Corruptions

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Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13507))

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Abstract

The Massive Parallel Computing (MPC) model gained wide adoption over the last decade. By now, it is widely accepted as the right model for capturing the commonly used programming paradigms (such as MapReduce, Hadoop, and Spark) that utilize parallel computation power to manipulate and analyze huge amounts of data.

Motivated by the need to perform large-scale data analytics in a privacy-preserving manner, several recent works have presented generic compilers that transform algorithms in the MPC model into secure counterparts, while preserving various efficiency parameters of the original algorithms. The first paper, due to Chan et al. (ITCS ’20), focused on the honest majority setting. Later, Fernando et al. (TCC ’20) considered the dishonest majority setting. The latter work presented a compiler that transforms generic MPC algorithms into ones which are secure against semi-honest attackers that may control all but one of the parties involved. The security of their resulting algorithm relied on the existence of a PKI and also on rather strong cryptographic assumptions: indistinguishability obfuscation and the circular security of certain LWE-based encryption systems.

In this work, we focus on the dishonest majority setting, following Fernando et al. In this setting, the known compilers do not achieve the standard security notion called malicious security, where attackers can arbitrarily deviate from the prescribed protocol. In fact, we show that unless very strong setup assumptions as made (such as a programmable random oracle), it is provably impossible to withstand malicious attackers due to the stringent requirements on space and round complexity.

As our main contribution, we complement the above negative result by designing the first general compiler for malicious attackers in the dishonest majority setting. The resulting protocols withstand all-but-one corruptions. Our compiler relies on a simple PKI and a (programmable) random oracle, and is proven secure assuming LWE and SNARKs. Interestingly, even with such strong assumptions, it is rather non-trivial to obtain a secure protocol.

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Notes

  1. 1.

    Throughout this paper, whenever the acronym MPC is used, it means “Massively Parallel Computation” and not “Multi-Party Computation”.

  2. 2.

    Some works design “communication preserving” secure computation protocols (for example, [44, 50, 55]) where the goal is to eliminate input/output-size dependency in communication complexity-all of these works only address the two parties setting.

  3. 3.

    In a leveled scheme the key and ciphertext sizes grow with the depth of the circuit being evaluated. In contrast, in a non-leveled scheme these sizes depend only on the security parameter. Gentry’s bootstrapping requires the assumption that ciphertexts remain semantically secure even when we use the encryption scheme to encrypt the secret decryption key.

  4. 4.

    Recall that no party knows the master secret key and so an inner short-output protocol is executed. Its inputs include the shares of the master secret key and it outputs an obfuscation of the aforementioned circuit.

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Acknowledgements

Rex Fernando is supported in part from a Simons Investigator Award, DARPA SIEVE award, NTT Research, NSF Frontier Award 1413955, BSF grant 2018393, a Xerox Faculty Research Award, a Google Faculty Research Award, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through Award HR00112020024. Yuval Gelles and Ilan Komargodski are supported in part by an Alon Young Faculty Fellowship, by a JPM Faculty Research Award, by a grant from the Israel Science Foundation (ISF Grant No. 1774/20), and by a grant from the US-Israel Binational Science Foundation and the US National Science Foundation (BSF-NSF Grant No. 2020643). Elaine Shi is supported in part by the US National Science Foundation (NSF awards 2044679 and 2128519).

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Authors and Affiliations

  1. UCLA, Los Angeles, USA

    Rex Fernando

  2. Hebrew University, Jerusalem, Israel

    Yuval Gelles & Ilan Komargodski

  3. NTT Research, Sunnyvale, USA

    Ilan Komargodski

  4. Carnegie Mellon University, Pittsburgh, USA

    Elaine Shi

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  1. Rex Fernando
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  2. Yuval Gelles
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Correspondence to Rex Fernando .

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Editors and Affiliations

  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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Fernando, R., Gelles, Y., Komargodski, I., Shi, E. (2022). Maliciously Secure Massively Parallel Computation for All-but-One Corruptions. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13507. Springer, Cham. https://doi.org/10.1007/978-3-031-15802-5_24

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