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Fully-Secure MPC with Minimal Trust

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13748))

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Abstract

The task of achieving full security (with guaranteed output delivery) in secure multiparty computation (MPC) is a long-studied problem. Known impossibility results (Cleve, STOC 86) rule out general solutions in the dishonest majority setting. In this work, we consider solutions that use an external trusted party (TP) to bypass the impossibility results, and study the minimal requirements needed from this trusted party. In particular, we restrict ourselves to the extreme setting where the size of the TP is independent of the size of the functionality to be computed (called “small" TP) and this TP is invoked only once during the protocol execution. We present several positive and negative results for fully-secure MPC in this setting.

  • For a natural class of protocols, specifically, those with a universal output decoder, we show that the size of the TP must necessarily be exponential in the number of parties. This result holds irrespective of the computational assumptions used in the protocol. The class of protocols to which our lower bound applies is broad enough to capture prior results in the area, implying that the prior techniques necessitate the use of an exponential-sized TP. We additionally rule out the possibility of achieving information-theoretic full security (without the restriction of using a universal output decoder) using a “small" TP in the plain model (i.e., without any setup).

  • In order to get around the above negative result, we consider protocols without a universal output decoder. The main positive result in our work is a construction of such a fully-secure MPC protocol assuming the existence of a succinct Functional Encryption scheme. We also give evidence that such an assumption is likely to be necessary for fully-secure MPC in certain restricted settings.

  • Finally, we explore the possibility of achieving full-security with a semi-honest TP that could collude with other malicious parties (which form a dishonest majority). In this setting, we show that even fairness is impossible to achieve regardless of the “small TP” requirement.

S. Patranabis—Most of the work was done while the author was affiliated with ETH Zürich, Switzerland and Visa Research USA.

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Notes

  1. 1.

    This notion differs from the line of work on token-based cryptography initiated by Katz [Kat07], where the tamper-proof tokens are generated locally, and the main challenge is to guarantee security even when tokens can be maliciously generated.

  2. 2.

    The notion of fail-stop corruption lies between semi-honest and malicious corruption, where eavesdropping like semi-honest corruption is allowed and the only possible malicious corruption is stopping the execution of the protocol.

  3. 3.

    Some of the protocols in the literature realizing this functionality for general functions are [GS18].

  4. 4.

    We believe that a non-interactive post-TP computation phase is essentially without loss of generality. In other words, any fully secure MPC protocol (having access to one TP call) with interaction amongst the parties can be transformed to one where the parties do not communicate at all amongst themselves after receiving TP’s response. We give a proof in the full version of our paper.

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Acknowledgments

We thank the anonymous reviewers of TCC 2022 for their helpful comments and suggestions. Y. Ishai was supported in part by ERC Project NTSC (742754), BSF grant 2018393, and ISF grant 2774/20. A. Patra would like to acknowledge financial support from DST National Mission on Interdisciplinary Cyber-Physical Systems (NM-ICPS) 2020–2025. D. Ravi was funded by the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme under grant agreement No 803096 (SPEC). A. Srinivasan was supported in part by a SERB startup grant.

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Authors and Affiliations

  1. Technion, Haifa, Israel

    Yuval Ishai

  2. Indian Institute of Science, Bangalore, India

    Arpita Patra

  3. IBM Research India, Bangalore, India

    Sikhar Patranabis

  4. Aarhus University, Aarhus, Denmark

    Divya Ravi

  5. Tata Institute of Fundamental Research, Mumbai, India

    Akshayaram Srinivasan

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Correspondence to Divya Ravi .

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  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Ishai, Y., Patra, A., Patranabis, S., Ravi, D., Srinivasan, A. (2022). Fully-Secure MPC with Minimal Trust. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13748. Springer, Cham. https://doi.org/10.1007/978-3-031-22365-5_17

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