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Two-Round Maliciously Secure Computation with Super-Polynomial Simulation

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Theory of Cryptography (TCC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13042))

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Abstract

We propose the first maliciously secure multi-party computation (MPC) protocol for general functionalities in two rounds, without any trusted setup. Since polynomial-time simulation is impossible in two rounds, we achieve the relaxed notion of superpolynomial-time simulation security [Pass, EUROCRYPT 2003]. Prior to our work, no such maliciously secure protocols were known even in the two-party setting for functionalities where both parties receive outputs. Our protocol is based on the sub-exponential security of standard assumptions plus a special type of non-interactive non-malleable commitment.

At the heart of our approach is a two-round multi-party conditional disclosure of secrets (MCDS) protocol in the plain model from bilinear maps, which is constructed from techniques introduced in [Benhamouda and Lin, TCC 2020].

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Notes

  1. 1.

    Running two instances of the same protocol in parallel does not achieve any meaningful security guarantee since nothing prevents one party from using two different inputs in each session.

  2. 2.

    We note that our usage of bilinear group based NIWI does not require any setup phase as the prover can self sample the group. Soundness of NIWI will hold as long as the group is cyclic and of the right order[GOS06b]. Also, our usage of tag-based non-malleable commitment scheme doesn’t require setup as the parties can locally choose their identities.

  3. 3.

    Specifically, we assume (a strengthened form of) sub-exponentially secure non-malleable commitments with respect to commitment.

  4. 4.

    Semi-malicious security is a strengthening of semi-honest security where the adversary follows the specifications of the protocols but can choose the random coins of the corrupted parties arbitrarily.

  5. 5.

    This is needed, for example, to ensure that the hybrid before switching to trapdoor is indistinguishable from the hybrid obtained after switching to trapdoor w.r.t an adversary who was unable to retrieve the Round 2 semi-malicious MPC message in the former hybrid (because of some dishonest behavior in the Round 1). We would like to avoid a scenario where such an adversary is actively trying to maul the honest party’s \(C_i^H\) into its own \(C_i^M\) and therefore distinguishes the latter hybrid from the former one (by successfully retrieving the Round 2 MPC message in the latter but not the former).

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Author information

Authors and Affiliations

  1. University of Illinois Urbana Champaign, Illinois, USA

    Amit Agarwal & Dakshita Khurana

  2. UC Berkeley, Berkeley, USA

    James Bartusek

  3. Carnegie Mellon University and NTT Research, Pittsburgh, USA

    Vipul Goyal

  4. Max Planck Institute for Security and Privacy, Bochum, Germany

    Giulio Malavolta

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  1. Amit Agarwal
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  5. Giulio Malavolta
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Correspondence to Amit Agarwal .

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Editors and Affiliations

  1. Georgetown University, Washington, WA, USA

    Kobbi Nissim

  2. The University of Texas at Austin, Austin, TX, USA

    Brent Waters

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Agarwal, A., Bartusek, J., Goyal, V., Khurana, D., Malavolta, G. (2021). Two-Round Maliciously Secure Computation with Super-Polynomial Simulation. In: Nissim, K., Waters, B. (eds) Theory of Cryptography. TCC 2021. Lecture Notes in Computer Science(), vol 13042. Springer, Cham. https://doi.org/10.1007/978-3-030-90459-3_22

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