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Network Agnostic MPC with Statistical Security

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Theory of Cryptography (TCC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14370))

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Abstract

In this work, we initiate the study of network agnostic MPC protocols with statistical security. Network agnostic MPC protocols give the best possible security guarantees, irrespective of the behaviour of the underlying network. While network agnostic MPC protocols have been designed earlier with perfect and computational security, nothing is known in the literature regarding their possibility with statistical security. We consider the general-adversary model, where the adversary is characterized by an adversary structure which enumerates all possible candidate subsets of corrupt parties. Known statistically-secure synchronous MPC (SMPC) and asynchronous MPC (AMPC) protocols are secure against adversary structures satisfying the \(\mathbb {Q}^{(2)}\) and \(\mathbb {Q}^{(3)}\) conditions respectively, meaning that the union of no two and three subsets from the adversary structure cover the entire set of parties.

Fix adversary structures \(\mathcal {Z}_s\) and \(\mathcal {Z}_a\), satisfying the \(\mathbb {Q}^{(2)}\) and \(\mathbb {Q}^{(3)}\) conditions respectively, where \(\mathcal {Z}_a \subset \mathcal {Z}_s\). Then given an unconditionally-secure PKI, we ask whether it is possible to design a statistically-secure MPC protocol, which is resilient against \(\mathcal {Z}_s\) and \(\mathcal {Z}_a\) in a synchronous and an asynchronous network respectively, even if the parties are unaware of the network type. We show that this is possible iff \(\mathcal {Z}_s\) and \(\mathcal {Z}_a\) satisfy the \(\mathbb {Q}^{(2, 1)}\) condition, meaning that the union of any two subsets from \(\mathcal {Z}_s\) and any one subset from \(\mathcal {Z}_a\) is a proper subset of the set of parties. The complexity of our protocol is polynomial in \(|\mathcal {Z}_s|\).

A. Appan—Work done as a student at IIIT Bangalore.

A. Choudhury—This research is an outcome of the R &D work undertaken in the project under the Visvesvaraya PhD Scheme of Ministry of Electronics & Information Technology, Government of India, being implemented by Digital India Corporation.

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Notes

  1. 1.

    Actually, the overview was for \(\varPi _\textsf{Rand}\), but the same idea is also used in \(\varPi _\textsf{MDVSS}\).

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Author information

Authors and Affiliations

  1. University of Illinois Urbana Champaign, Champaign, USA

    Ananya Appan

  2. International Institute of Information Technology Bangalore, Bengaluru, India

    Ashish Choudhury

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  1. Ananya Appan
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  2. Ashish Choudhury
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Correspondence to Ananya Appan .

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  1. Apple, Cupertino, CA, USA

    Guy Rothblum

  2. NTT Research, Sunnyvale, CA, USA

    Hoeteck Wee

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© 2023 International Association for Cryptologic Research

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Appan, A., Choudhury, A. (2023). Network Agnostic MPC with Statistical Security. In: Rothblum, G., Wee, H. (eds) Theory of Cryptography. TCC 2023. Lecture Notes in Computer Science, vol 14370. Springer, Cham. https://doi.org/10.1007/978-3-031-48618-0_3

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  • DOI: https://doi.org/10.1007/978-3-031-48618-0_3

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