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Three-Round Secure Multiparty Computation from Black-Box Two-Round Oblivious Transfer

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Advances in Cryptology – CRYPTO 2021 (CRYPTO 2021)

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Abstract

We give constructions of three-round secure multiparty computation (MPC) protocols for general functions that make black-box use of a two-round oblivious transfer (OT). For the case of semi-honest adversaries, we make use of a two-round, semi-honest secure OT in the plain model. This resolves the round-complexity of black-box (semi-honest) MPC protocols from minimal assumptions and answers an open question of Applebaum et al. (ITCS 2020). For the case of malicious adversaries, we make use of a two-round maliciously-secure OT in the common random/reference string model that satisfies a (mild) variant of adaptive security for the receiver.

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Notes

  1. 1.

    Here, we need to additionally ensure that malicious \(P_3\) is generating the shares correctly. Hence, we make use of a pairwise verifiable secret sharing based on bivariate polynomials and do additional checks on the shares to ensure that the sharing is done correctly.

  2. 2.

    Randomized protocols can be handled by including the randomness used by a party as part of its input.

  3. 3.

    Here, we slightly differ from the formulation used in [17, 19]. In their work, \(\mathsf {pre}\) is defined to additionally take \(x_i\) as input and outputs \((z_i,v_i)\). However, the transformation from any protocol to a conforming protocol given in these works has the above structure where the last \(\ell /n - m\) bits of \(z_i\) are 0 and the first m bits of \(z_i\) is the XOR of \(x_i\) and \(v_i[(i-1)\ell /n +1,(i-1)\ell /n +m]\).

  4. 4.

    We note that this property can be generically added to any conforming protocol by expanding the computation phase to include more actions that compute the output of the protocol.

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Authors and Affiliations

  1. Indian Institute of Science, Bangalore, India

    Arpita Patra

  2. Tata Institute of Fundamental Research, Mumbai, India

    Akshayaram Srinivasan

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  1. Arpita Patra
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Correspondence to Arpita Patra .

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

    Tal Malkin

  2. University of Michigan, Ann Arbor, MI, USA

    Chris Peikert

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Patra, A., Srinivasan, A. (2021). Three-Round Secure Multiparty Computation from Black-Box Two-Round Oblivious Transfer. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12826. Springer, Cham. https://doi.org/10.1007/978-3-030-84245-1_7

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  • DOI: https://doi.org/10.1007/978-3-030-84245-1_7

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