{"id":368519,"date":"2017-03-02T12:34:39","date_gmt":"2017-03-02T20:34:39","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=368519"},"modified":"2018-10-16T21:37:39","modified_gmt":"2018-10-17T04:37:39","slug":"secure-computation-minimal-interaction-revisited","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/secure-computation-minimal-interaction-revisited\/","title":{"rendered":"Secure Computation with Minimal Interaction, Revisited"},"content":{"rendered":"

Motivated by the goal of improving the concrete efficiency of secure multiparty computation (MPC), we revisit the question of MPC with only two rounds of interaction. We consider a minimal setting in which parties can communicate over secure point-to-point channels and where no broadcast channel or other form of setup is available.<\/p>\n

Katz and Ostrovsky (Crypto 2004) obtained negative results for such protocols with n<\/mi>=<\/mo>2<\/mn><\/math>\">n<\/span>=<\/span>2<\/span><\/span><\/span>n=2<\/span><\/span><\/span> parties. Ishai et al. (Crypto 2010) showed that if only one party may be corrupted, then n<\/mi>≥<\/mo>5<\/mn><\/math>\">n<\/span>\u2265<\/span>5<\/span><\/span><\/span>n\u22655<\/span><\/span><\/span> parties can securely compute any function in this setting, with guaranteed output delivery, assuming one-way functions exist. In this work, we complement the above results by presenting positive and negative results for the cases where n<\/mi>=<\/mo>3<\/mn><\/math>\">n<\/span>=<\/span>3<\/span><\/span><\/span>n=3<\/span><\/span><\/span> or n<\/mi>=<\/mo>4<\/mn><\/math>\">n<\/span>=<\/span>4<\/span><\/span><\/span>n=4<\/span><\/span><\/span> and where there is a single malicious party<\/em>.<\/p>\n

When n<\/mi>=<\/mo>3<\/mn><\/math>\">n<\/span>=<\/span>3<\/span><\/span><\/span>n=3<\/span><\/span><\/span>, we show a 2-round protocol which is secure with \u201cselective abort\u201d against a single malicious party. The protocol makes a black-box use of a pseudorandom generator or alternatively can offer unconditional security for functionalities in N<\/mi>C<\/mi><\/mrow>1<\/mn><\/msup><\/math>\">N<\/span>C<\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>NC1<\/span><\/span><\/span>. The concrete efficiency of this protocol is comparable to the efficiency of secure two-party computation protocols for semi-honest<\/em> parties based on garbled circuits.<\/p>\n

\n

When n<\/mi>=<\/mo>4<\/mn><\/math>\">n<\/span>=<\/span>4<\/span><\/span><\/span>n=4<\/span><\/span><\/span> in the setting described above, we show the following:<\/p>\n

\n
    \n
  • \n

    A statistical VSS<\/em> protocol that has a\u00a01-round sharing phase and 1-round reconstruction phase. This improves over the state-of-the-art result of Patra et al.\u00a0(Crypto 2009) whose VSS protocol required 2 rounds in the reconstruction phase.<\/p>\n<\/li>\n

  • \n

    A 2-round statistically secure protocol for linear functionalities<\/em> with guaranteed output delivery. This implies a 2-round 4-party fair coin\u00a0tossing protocol. We complement this by a negative result, showing that there is a (nonlinear) function for which there is no 2-round statistically secure protocol.<\/p>\n<\/li>\n

  • \n

    A 2-round computationally secure protocol for general functionalities<\/em> with guaranteed output delivery, under the assumption that injective (one-to-one) one-way functions exist.<\/p>\n<\/li>\n

  • \n

    A 2-round protocol for general functionalities with guaranteed output delivery in the preprocessing model<\/em>, whose correlated randomness complexity is proportional to the length of the inputs. This protocol makes a black-box use of a pseudorandom generator or alternatively can offer unconditional security for functionalities in N<\/mi>C<\/mi><\/mrow>1<\/mn><\/msup><\/math>\">N<\/span>C<\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>NC1<\/span><\/span><\/span>.<\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n

    Prior to our work, the feasibility results implied by our positive results were not known to hold even in the stronger MPC model considered by Gennaro et al.\u00a0(Crypto 2002), where a broadcast channel is available.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Motivated by the goal of improving the concrete efficiency of secure multiparty computation (MPC), we revisit the question of MPC with only two rounds of interaction. We consider a minimal setting in which parties can communicate over secure point-to-point channels and where no broadcast channel or other form of setup is available. Katz and Ostrovsky […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Springer, Berlin, Heidelberg","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"359-378","msr_page_range_start":"359","msr_page_range_end":"378","msr_series":"","msr_volume":"9216","msr_copyright":"","msr_conference_name":"Advances in Cryptology - CRYPTO 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