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

Authors Rex Fernando , Yuval Gelles , Ilan Komargodski

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Author Details

Rex Fernando
  • Aptos Labs, Palo Alto, CA, USA
Yuval Gelles
  • The Hebrew University of Jerusalem, Israel
Ilan Komargodski
  • The Hebrew University of Jerusalem, Israel
  • NTT Research, Sunnyvale, CA, USA

Funding

  • Fernando, Rex: Algorand Centres of Excellence (ACE) Programme, the Defense Advanced Research Projects Agency under award number HR001120C0086, the Office of Naval Research under award number N000142212064, and the National Science Foundation under award numbers 2128519 and 2044679. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.
  • Gelles, Yuval: ISF Grant No. 1774/20 and BSF-NSF Grant No. 2020643.
  • Komargodski, Ilan: Alon Young Faculty Fellowship, ISF Grant No. 1774/20, and BSF-NSF Grant No. 2020643.

Acknowledgements

We thank the anonymous reviewers for instructive suggestions.

Cite AsGet BibTex

Rex Fernando, Yuval Gelles, and Ilan Komargodski. Scalable Distributed Agreement from LWE: Byzantine Agreement, Broadcast, and Leader Election. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 46:1-46:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.46

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 Õ(√ n) per-party communication and Õ(1) rounds, where n stands for the number of parties, tolerating 1/3-ε 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 Õ(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 Õ(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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
  • Theory of computation → Distributed algorithms
Keywords
  • Byzantine agreement
  • scalable
  • learning with errors

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