Round-Optimal Secure Multi-Party Computation

  • Shai HaleviEmail author
  • Carmit Hazay
  • Antigoni Polychroniadou
  • Muthuramakrishnan Venkitasubramaniam
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10992)


Secure multi-party computation (MPC) is a central cryptographic task that allows a set of mutually distrustful parties to jointly compute some function of their private inputs where security should hold in the presence of a malicious adversary that can corrupt any number of parties. Despite extensive research, the precise round complexity of this “standard-bearer” cryptographic primitive is unknown. Recently, Garg, Mukherjee, Pandey and Polychroniadou, in EUROCRYPT 2016 demonstrated that the round complexity of any MPC protocol relying on black-box proofs of security in the plain model must be at least four. Following this work, independently Ananth, Choudhuri and Jain, CRYPTO 2017 and Brakerski, Halevi, and Polychroniadou, TCC 2017 made progress towards solving this question and constructed four-round protocols based on non-polynomial time assumptions. More recently, Ciampi, Ostrovsky, Siniscalchi and Visconti in TCC 2017 closed the gap for two-party protocols by constructing a four-round protocol from polynomial-time assumptions. In another work, Ciampi, Ostrovsky, Siniscalchi and Visconti TCC 2017 showed how to design a four-round multi-party protocol for the specific case of multi-party coin-tossing.

In this work, we resolve this question by designing a four-round actively secure multi-party (two or more parties) protocol for general functionalities under standard polynomial-time hardness assumptions with a black-box proof of security.


Secure multi-party computation Garbled circuits Round complexity Additive errors 



We thank the anonymous reviewers for their valuable feedback. Following Ananth et. al. [ACJ17], we would like to acknowledge Yuval Ishai’s contribution in the three-bit three-round multiplication protocol employed in this work. We would also like to thank Daniel Genkin, Yuval Ishai and Mor Weiss for several discussions on binary AMD resilient circuits.

The first author was supported by the Defense Advanced Research Projects Agency (DARPA) and Army Research Office(ARO) under Contract No. W911NF-15-C-0236. The second author was supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office. The third author was supported by the National Science Foundation under Grant No. 1617676, 1526377 and 1618884, IBM under Agreement 4915013672 and the Packard Foundation under Grant 2015-63124. The last author was supported by the National Science Foundation under Grant No. 1526377 and 1618884, a Google Faculty Research grant and DIMACS Special Focus on Cryptography program. The work was partially done while the fourth author was at Cornell Tech.

The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense, the National Science Foundation, or the U.S. Government.


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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Shai Halevi
    • 1
    Email author
  • Carmit Hazay
    • 2
  • Antigoni Polychroniadou
    • 3
  • Muthuramakrishnan Venkitasubramaniam
    • 4
  1. 1.IBM ResearchNew YorkUSA
  2. 2.Bar-Ilan UniversityRamat GanIsrael
  3. 3.Cornell Tech and University of RochesterNew YorkUSA
  4. 4.University of RochesterNew YorkUSA

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