Secure multiparty computation with minimal interaction

Yuval Ishai, Eyal Kushilevitz, Anat Paskin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

39 Scopus citations


We revisit the question of secure multiparty computation (MPC) with two rounds of interaction. It was previously shown by Gennaro et al. (Crypto 2002) that 3 or more communication rounds are necessary for general MPC protocols with guaranteed output delivery, assuming that there may be t ≥ 2 corrupted parties. This negative result holds regardless of the total number of parties, even if broadcast is allowed in each round, and even if only fairness is required. We complement this negative result by presenting matching positive results. Our first main result is that if only one party may be corrupted, then n ≥ 5 parties can securely compute any function of their inputs using only two rounds of interaction over secure point-to-point channels (without broadcast or any additional setup). The protocol makes a black-box use of a pseudorandom generator, or alternatively can offer unconditional security for functionalities in NC1. We also prove a similar result in a client-server setting, where there are m ≥ 2 clients who hold inputs and should receive outputs, and n additional servers with no inputs and outputs. For this setting, we obtain a general MPC protocol which requires a single message from each client to each server, followed by a single message from each server to each client. The protocol is secure against a single corrupted client and against coalitions of t<n/3 corrupted servers. The above protocols guarantee output delivery and fairness. Our second main result shows that under a relaxed notion of security, allowing the adversary to selectively decide (after learning its own outputs) which honest parties will receive their (correct) output, there is a general 2-round MPC protocol which tolerates t<n/3 corrupted parties. This protocol relies on the existence of a pseudorandom generator in NC1 (which is implied by standard cryptographic assumptions), or alternatively can offer unconditional security for functionalities in NC1.

Original languageEnglish
Title of host publicationAdvances in Cryptology - CRYPTO 2010 - 30th Annual Cryptology Conference, Proceedings
Number of pages18
StatePublished - 2010
Externally publishedYes
Event30th Annual International Cryptology Conference, CRYPTO 2010 - Santa Barbara, CA, United States
Duration: 15 Aug 201019 Aug 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6223 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference30th Annual International Cryptology Conference, CRYPTO 2010
Country/TerritoryUnited States
CitySanta Barbara, CA


  • Secure multiparty computation
  • round complexity


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