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Black-Box Constructions of Bounded-Concurrent Secure Computation

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Security and Cryptography for Networks (SCN 2020)

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Abstract

We construct a general purpose secure multiparty computation protocol which remains secure under (a-priori) bounded-concurrent composition and makes only black-box use of cryptographic primitives. Prior to our work, constructions of such protocols required non-black-box usage of cryptographic primitives; alternatively, black-box constructions could only be achieved for super-polynomial simulation based notions of security which offer incomparable security guarantees.

Our protocol has a constant number of rounds and relies on standard polynomial-hardness assumptions, namely, the existence of semi-honest oblivious transfers and collision-resistant hash functions. Previously, such protocols were not known even under sub-exponential assumptions.

S. Garg—Supported in part from DARPA SIEVE Award, AFOSR Award FA9550-15-1-0274, AFOSR Award FA9550-19-1-0200, AFOSR YIP Award, NSF CNS Award 1936826, DARPA and SPAWAR under contract N66001-15-C-4065, a Hellman Award, a Sloan Research Fellowship and research grants by the Okawa Foundation, Visa Inc., and Center for Long-Term Cybersecurity (CLTC, UC Berkeley). The views expressed are those of the author and do not reflect the official policy or position of the funding agencies.

X. Liang and O. Pandey—Supported in part by DARPA SIEVE Award HR00112020026, NSF grant 1907908, and a Cisco Research Award. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government, DARPA, NSF, or Cisco.

I. Visconti—This research has been supported in part by the European Union’s Horizon 2020 research and innovation programme under grant agreement No 780477 (project PRIViLEDGE.

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Notes

  1. 1.

    It means the extraction strategy does not involve rewinding techniques.

  2. 2.

    In some works, when the construction is black-box but the proof of security uses non-black-box techniques (as in this paper), this is referred to as a semi-black-box protocol.

  3. 3.

    In their original construction, C sends a trapdoor permutation (TDP) f and then proves in zero-knowledge that f is indeed a valid TDP. To make this step black-box, C can send an enhanced TDP instead (without the need of \(\mathcal {ZK}\) proof).

  4. 4.

    In [31], this commitment is actually required to be statistically-hiding. But it can be replaced with a statistically-binding scheme if certain modifications are made to the proof phase. See [24] for more details.

  5. 5.

    Note \(I_x(y) = 1\) if and only if \(y=x\) is well defined and the “code” of \(I_x\) requires only the knowledge of x.

  6. 6.

    Note that we cannot ask the committer to prove in zero-knowledge that he uses the committed shares as sender’s input in the OT execution, because such proof will make non-black-box use of both the commitment and OT.

  7. 7.

    A related but very different notion of robustness appears explicitly in the context of non-malleability in [30, 42].

  8. 8.

    We remark that this step can actually happen in parallel with the \(\mathsf {OT}\) instances in Step 3. It is put here (only) to ease the presentation of the security proof. In [24], we talk about how the proof can be modified to accommodate the case where the Step-4 \(\mathsf {OT}\) happens in parallel with Step 3.

  9. 9.

    Note that the security of Step-5 coin tossing ensures that \(R^*\) can learn both (decommitments to) \(s_{n,0}\) and \(s_{n,1}\) with only negligible probability.

  10. 10.

    The protocol of Ishai et al. [36] itself does not satisfy the above property, but as shown in [22], it can be easily modified to satisfy it.

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Authors and Affiliations

  1. University of California, Berkeley, USA

    Sanjam Garg

  2. Stony Brook University, Stony Brook, USA

    Xiao Liang & Omkant Pandey

  3. University of Salerno, Fisciano, Italy

    Ivan Visconti

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  1. Sanjam Garg
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Correspondence to Xiao Liang .

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  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

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

    Vladimir Kolesnikov

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Garg, S., Liang, X., Pandey, O., Visconti, I. (2020). Black-Box Constructions of Bounded-Concurrent Secure Computation. 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_5

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