Scalable Distributed Agreement from LWE: Byzantine Agreement, Broadcast, and Leader Election

Rex Fernando*, Yuval Gelles*, Ilan Komargodski*

*Corresponding author for this work

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

Abstract

Distributed agreement is a general name for the task of ensuring consensus among non-faulty nodes in the presence of faulty or malicious behavior. Well-known instances of agreement tasks are Byzantine Agreement, Broadcast, and Committee or Leader Election. Since agreement tasks lie at the heart of many modern distributed applications, there has been an increased interest in designing scalable protocols for these tasks. Specifically, we want protocols where the per-party communication complexity scales sublinearly with the number of parties. With unconditional security, the state of the art protocols have O (√ n) per-party communication and O(1) rounds, where n stands for the number of parties, tolerating 1/3ϵ fraction of corruptions for any ϵ >0. There are matching lower bounds showing that these protocols are essentially optimal among a large class of protocols. Recently, Boyle-Cohen-Goel (PODC 2021) relaxed the attacker to be computationally bounded and using strong cryptographic assumptions showed a protocol with O (1) per-party communication and rounds (similarly, tolerating 1/3 ϵ fraction of corruptions). The security of their protocol relies on SNARKs for NP with linear-Time extraction, a somewhat strong and non-standard assumption. Their protocols further relies on a public-key infrastructure (PKI) and a common-reference-string (CRS). In this work, we present a new protocol with O (1) per-party communication and rounds but relying only on the standard Learning With Errors (LWE) assumption. Our protocol also relies on a PKI and a CRS, and tolerates 1/3 ϵ fraction of corruptions, similarly to Boyle et al. Technically, we leverage (multi-hop) BARGs for NP directly and in a generic manner which significantly deviate from the framework of Boyle et al.

Original languageAmerican English
Title of host publication15th Innovations in Theoretical Computer Science Conference, ITCS 2024
EditorsVenkatesan Guruswami
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773096
DOIs
StatePublished - Jan 2024
Event15th Innovations in Theoretical Computer Science Conference, ITCS 2024 - Berkeley, United States
Duration: 30 Jan 20242 Feb 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume287
ISSN (Print)1868-8969

Conference

Conference15th Innovations in Theoretical Computer Science Conference, ITCS 2024
Country/TerritoryUnited States
CityBerkeley
Period30/01/242/02/24

Bibliographical note

Publisher Copyright:
© 2024 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

Keywords

  • Byzantine agreement
  • learning with errors
  • scalable

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