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The Round Complexity of Secure Computation Against Covert Adversaries

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Security and Cryptography for Networks (SCN 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12238))

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Abstract

We investigate the exact round complexity of secure multiparty computation (MPC) against covert adversaries who may attempt to cheat, but do not wish to be caught doing so. Covert adversaries lie in between semi-honest adversaries who follow protocol specification and malicious adversaries who may deviate arbitrarily.

Recently, two round protocols for semi-honest MPC and four round protocols for malicious-secure MPC were constructed, both of which are optimal. While these results can be viewed as constituting two end points of a security spectrum, we investigate the design of protocols that potentially span the spectrum.

Our main result is an MPC protocol against covert adversaries with variable round complexity: when the detection probability is set to the lowest setting, our protocol requires two rounds and offers same security as semi-honest MPC. By increasing the detecting probability, we can increase the security guarantees, with round complexity five in the extreme case. The security of our protocol is based on standard cryptographic assumptions.

We supplement our positive result with a negative result, ruling out strict three round protocols with respect to black-box simulation.

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Notes

  1. 1.

    The work of [3] also provides two other formulations of security. In this work, we focus on the above formulation.

  2. 2.

    One may ask whether modeling protocol abort as cheating could lead to scenarios where honest parties, in the presence of network interruptions, are labeled as adversarial. We imagine that in such a scenario, one could put in place countermeasures, where, e.g., a party is allowed to prove (in zero knowledge) honest behavior in the protocol (up to the point of purported abort) to other parties in order to defend itself.

  3. 3.

    This in particular means we cannot ignore the verifier’s last message to transform the protocol to a three round protocol in the alternating message model as in [15].

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Acknowledgments

Vipul Goyal is supported in part by the NSF award 1916939, a gift from Ripple, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award.

Arka Rai Choudhuri and Abhishek Jain are supported in part by DARPA/ARL Safeware Grant W911NF-15-C-0213, NSF CNS-1814919, NSF CAREER 1942789, Samsung Global Research Outreach award and Johns Hopkins University Catalyst award. Arka Rai Choudhuri is also supported by NSF Grants CNS-1908181 and CNS-1414023.

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Authors and Affiliations

  1. Johns Hopkins University, Baltimore, USA

    Arka Rai Choudhuri & Abhishek Jain

  2. Carnegie Mellon University, Pittsburgh, USA

    Vipul Goyal

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  1. Arka Rai Choudhuri
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Correspondence to Arka Rai Choudhuri .

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Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

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Choudhuri, A.R., Goyal, V., Jain, A. (2020). The Round Complexity of Secure Computation Against Covert Adversaries. In: Galdi, C., Kolesnikov, V. (eds) Security and Cryptography for Networks. SCN 2020. Lecture Notes in Computer Science(), vol 12238. Springer, Cham. https://doi.org/10.1007/978-3-030-57990-6_30

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