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The Exact Round Complexity of Secure Computation

  • Sanjam GargEmail author
  • Pratyay Mukherjee
  • Omkant Pandey
  • Antigoni Polychroniadou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9666)

Abstract

We revisit the exact round complexity of secure computation in the multi-party and two-party settings. For the special case of two-parties without a simultaneous message exchange channel, this question has been extensively studied and resolved. In particular, Katz and Ostrovsky (CRYPTO ’04) proved that 5 rounds are necessary and sufficient for securely realizing every two-party functionality where both parties receive the output. However, the exact round complexity of general multi-party computation, as well as two-party computation with a simultaneous message exchange channel, is not very well understood.

These questions are intimately connected to the round complexity of non-malleable commitments. Indeed, the exact relationship between the round complexities of non-malleable commitments and secure multi-party computation has also not been explored.

In this work, we revisit these questions and obtain several new results. First, we establish the following main results. Suppose that there exists a k-round non-malleable commitment scheme, and let \(k'=\max (4,k+1)\); then,
  • (Two-party setting with simultaneous message transmission): there exists a \(k'\)-round protocol for securely realizing every two-party functionality;

  • (Multi-party setting): there exists a \(k'\)-round protocol for securely realizing the multi-party coin-flipping functionality.

As a corollary of the above results, by instantiating them with existing non-malleable commitment protocols (from the literature), we establish that four rounds are both necessary and sufficient for both the results above. Furthermore, we establish that, for every multi-party functionality five rounds are sufficient.

We actually obtain a variety of results offering trade-offs between rounds and the cryptographic assumptions used, depending upon the particular instantiations of underlying protocols.

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Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Sanjam Garg
    • 1
    Email author
  • Pratyay Mukherjee
    • 1
  • Omkant Pandey
    • 2
  • Antigoni Polychroniadou
    • 3
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.Drexel UniversityPhiladelphiaUSA
  3. 3.Aarhus UniversityAarhusDenmark

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