The round complexity of perfect mpc with active security and optimal resiliency

Benny Applebaum, Eliran Kachlon, Arpita Patra

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

Abstract

In STOC 1988, Ben-Or, Goldwasser, and Wigderson (BGW) established an important milestone in the fields of cryptography and distributed computing by showing that every functionality can be computed with perfect (information-theoretic and error-free) security at the presence of an active (aka Byzantine) rushing adversary that controls up to n/3 of the parties. We study the round complexity of general secure multiparty computation in the BGW model. Our main result shows that every functionality can be realized in only four rounds of interaction, and that some functionalities cannot be computed in three rounds. This completely settles the round-complexity of perfect actively-secure optimally-resilient MPC, resolving a long line of research. Our lower-bound is based on a novel round-reduction technique that allows us to lift existing three-round lower-bounds for verifiable secret sharing to four-round lower-bounds for general MPC. To prove the upper-bound, we develop new round-efficient protocols for computing degree-2 functionalities over large fields, and establish the completeness of such functionalities. The latter result extends the recent completeness theorem of Applebaum, Brakerski and Tsabary (TCC 2018, Eurocrypt 2019) that was limited to the binary field.

Original languageEnglish
Title of host publicationProceedings - 2020 IEEE 61st Annual Symposium on Foundations of Computer Science, FOCS 2020
PublisherIEEE Computer Society
Pages1277-1284
Number of pages8
ISBN (Electronic)9781728196213
DOIs
StatePublished - Nov 2020
Event61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020 - Virtual, Durham, United States
Duration: 16 Nov 202019 Nov 2020

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2020-November
ISSN (Print)0272-5428

Conference

Conference61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020
Country/TerritoryUnited States
CityVirtual, Durham
Period16/11/2019/11/20

Keywords

  • Cryptographic Protocols
  • Information-Theoretic Cryptography
  • Round Complexity
  • Secure Computation

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