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Revisiting Fairness in MPC: Polynomial Number of Parties and General Adversarial Structures

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

Abstract

We investigate fairness in secure multiparty computation when the number of parties \(n = {{\,\mathrm{poly}\,}}(\lambda )\) grows polynomially in the security parameter, \(\lambda \). Prior to this work, efficient protocols achieving fairness with no honest majority and polynomial number of parties were known only for the AND and OR functionalities (Gordon and Katz, TCC’09). We show the following:

  • We first consider symmetric Boolean functions \(F : \{0,1\}^n \rightarrow \{0,1\}\), where the underlying function \(f_{n/2,n/2}: \{0, \ldots , n/2\} \times \{0, \ldots , n/2\} \rightarrow \{0,1\}\) can be computed fairly and efficiently in the 2-party setting. We present an efficient protocol for any such F tolerating n/2 or fewer corruptions, for \(n = {{\,\mathrm{poly}\,}}(\lambda )\) number of parties.

  • We present an efficient protocol for n-party majority tolerating \(n/2+1\) or fewer corruptions, for \(n = {{\,\mathrm{poly}\,}}(\lambda )\) number of parties. The construction extends to \(n/2+c\) or fewer corruptions, for constant c.

  • We extend both of the above results to more general types of adversarial structures and present instantiations of non-threshold adversarial structures of these types. These instantiations are obtained via constructions of projective planes and combinatorial designs.

Supported in part by NSF grants #CNS-1933033, #CNS-1453045 (CAREER) and by financial assistance awards 70NANB15H328 and 70NANB19H126 from the U.S. Department of Commerce, National Institute of Standards and Technology.

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Notes

  1. 1.

    In this context, we mean a Boolean function whose output depends only on the number of ones in the input. See [36], Def. 2.8.

  2. 2.

    If \(N-z\) is an invalid input (i.e. \(N-z \notin \{0, \ldots , n/2\}\)), then the dealer simply uses dummy values.

  3. 3.

    We require an identifiable abort property to allow elimination of aborting/misbehaving parties and restarting of the protocol. Similar properties were needed in the work of [21]. They required secure computation with designated abort: If the output of the protocol is \(\bot \), the parties restart without the lowest indexed party. Also, if the protocol outputs a set \(\mathcal {S}\) (indicating those parties whose inputs were inconsistent), the set \(\mathcal {S}\) is eliminated.

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Dachman-Soled, D. (2020). Revisiting Fairness in MPC: Polynomial Number of Parties and General Adversarial Structures. 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_21

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