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TCC 2020: Theory of Cryptography pp 291–319Cite as

Round Optimal Secure Multiparty Computation from Minimal Assumptions

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

Abstract

We construct a four round secure multip arty computation (MPC) protocol in the plain model that achieves security against any dishonest majority. The security of our protocol relies only on the existence of four round oblivious transfer. This culminates the long line of research on constructing round-efficient MPC from minimal assumptions (at least w.r.t. black-box simulation).

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Fig. 1.
Fig. 2.

Notes

  1. 1.

    A detailed discussion on related works can be found in the full version.

  2. 2.

    Roughly speaking, such adversaries behave like semi-honest adversaries, except that they may choose arbitrary random tapes.

  3. 3.

    Roughly speaking, a delayed semi-malicious adversary is similar to semi-malicious adversary, except that in the second last round of a k-round protocol, it is required to output (on a special tape) a witness (namely, its input and randomness) that establishes its honest behavior in all the rounds so far.

  4. 4.

    There are some exceptions; we refer the reader to the full version for discussion on other models.

  5. 5.

    A proof system is said to be delayed input if the instance is only required for computing the last round of the proof.

  6. 6.

    That is, where the instances are sampled from a public distribution.

  7. 7.

    Note that if the protocol does progress to the fourth round, then we do not need to shield promise ZK anymore.

  8. 8.

    We note that this property was also used by [5] in their construction of k-round malicious-secure MPC.

  9. 9.

    The commitment scheme of [3] also achieves some security properties, in addition to bounded rewind security, that are not required by our compiler. Hence, we use a simplified variant of their scheme.

  10. 10.

    This means the extractor can output a non \(\perp \) value if the commitment has no valid opening.

  11. 11.

    These values can be obtained from the malicious sender via an expected PPT rewinding procedure. The expected PPT simulator in our applications performs the necessary rewindings and then feeds these values to the extractor \(\mathsf {TDExt}\).

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Acknowledgments

We would like to thank Alex Lombardi and Luke Schaeffer for pointing out to us that any OT with perfect completeness implies non-interactive commitment schemes, and, for suggesting to us to revise our theorem statements to reflect this observation. Vipul Goyal is supported in part by the NSF award 1916939, a gift from Ripple, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award. Arka Rai Choudhuri and Abhishek Jain are supported in part by DARPA/ARL Safeware Grant W911NF-15-C-0213, NSF CNS-1814919, NSF CAREER 1942789, Samsung Global Research Outreach award and Johns Hopkins University Catalyst award. Arka Rai Choudhuri is also supported by NSF Grants CNS-1908181, CNS-1414023, and the Office of Naval Research Grant N00014-19-1-2294. Rafail Ostrovsky is supported in part by NSF-BSF Grant 1619348, DARPA/SPAWAR N66001-15-C-4065, ODNI/IARPA 2019-1902070008 US-Israel BSF grant 2012366, JP Morgan Faculty Award, Google Faculty Research Award, OKAWA Foundation Research Award, IBM Faculty Research Award, Xerox Faculty Research Award, B. John Garrick Foundation Award, Teradata Research Award, and Lockheed-Martin Corporation Research Award. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official views or policies, either expressed or implied, of the Department of Defense, DARPA, ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein. Michele Ciampi was partially supported by H2020 project PRIVILEDGE #780477.

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Authors and Affiliations

  1. Johns Hopkins University, Baltimore, USA

    Arka Rai Choudhuri & Abhishek Jain

  2. The University of Edinburgh, Edinburgh, UK

    Michele Ciampi

  3. Carnegie Mellon University, Pittsburgh, USA

    Vipul Goyal

  4. NTT Research, East Palo Alto, USA

    Vipul Goyal

  5. University of California, Los Angeles, USA

    Rafail Ostrovsky

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  1. Arka Rai Choudhuri
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Correspondence to Arka Rai Choudhuri .

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Editors and Affiliations

  1. Cornell Tech, New York, NY, USA

    Prof. Rafael Pass

  2. Institute of Science and Technology Austria, Klosterneuburg, Austria

    Krzysztof Pietrzak

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Rai Choudhuri, A., Ciampi, M., Goyal, V., Jain, A., Ostrovsky, R. (2020). Round Optimal Secure Multiparty Computation from Minimal Assumptions. 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_11

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