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DOI: 10.4230/LIPIcs.ITCS.2024.46

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

Authors: Rex Fernando, Yuval Gelles, and Ilan Komargodski

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

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.

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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)

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@InProceedings{fernando_et_al:LIPIcs.ITCS.2024.46,
  author =	{Fernando, Rex and Gelles, Yuval and Komargodski, Ilan},
  title =	{{Scalable Distributed Agreement from LWE: Byzantine Agreement, Broadcast, and Leader Election}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{46:1--46:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.46},
  URN =		{urn:nbn:de:0030-drops-195744},
  doi =		{10.4230/LIPIcs.ITCS.2024.46},
  annote =	{Keywords: Byzantine agreement, scalable, learning with errors}
}

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Brief Announcement

DOI: 10.4230/LIPIcs.DISC.2023.42

Brief Announcement: Scalable Agreement Protocols with Optimal Optimistic Efficiency

Authors: Yuval Gelles and Ilan Komargodski

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract

Designing efficient distributed protocols for various agreement tasks such as Byzantine Agreement, Broadcast, and Committee Election is a fundamental problem. We are interested in scalable protocols for these tasks, where each (honest) party communicates a number of bits which is sublinear in n, the number of parties. The first major step towards this goal is due to King et al. (SODA 2006) who showed a protocol where each party sends only Õ(1) bits throughout Õ(1) rounds, but guarantees only that 1-o(1) fraction of honest parties end up agreeing on a consistent output, assuming constant < 1/3 fraction of static corruptions. Few years later, King et al. (ICDCN 2011) managed to get a full agreement protocol in the same model but where each party sends Õ(√n) bits throughout Õ(1) rounds. Getting a full agreement protocol with o(√n) communication per party has been a major challenge ever since. In light of this barrier, we propose a new framework for designing efficient agreement protocols. Specifically, we design Õ(1)-round protocols for all of the above tasks (assuming constant < 1/3 fraction of static corruptions) with optimistic and pessimistic guarantees: - Optimistic complexity: In an honest execution, all parties send only Õ(1) bits. - Pessimistic complexity: In any other case, (honest) parties send Õ(√n) bits. Thus, all an adversary can gain from deviating from the honest execution is that honest parties will need to work harder (i.e., transmit more bits) to reach agreement and terminate. Besides the above agreement tasks, we also use our new framework to get a scalable secure multiparty computation (MPC) protocol with optimistic and pessimistic complexities. Technically, we identify a relaxation of Byzantine Agreement (of independent interest) that allows us to fall-back to a pessimistic execution in a coordinated way by all parties. We implement this relaxation with Õ(1) communication bits per party and within Õ(1) rounds.

Cite as

Yuval Gelles and Ilan Komargodski. Brief Announcement: Scalable Agreement Protocols with Optimal Optimistic Efficiency. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 42:1-42:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gelles_et_al:LIPIcs.DISC.2023.42,
  author =	{Gelles, Yuval and Komargodski, Ilan},
  title =	{{Brief Announcement: Scalable Agreement Protocols with Optimal Optimistic Efficiency}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{42:1--42:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.42},
  URN =		{urn:nbn:de:0030-drops-191684},
  doi =		{10.4230/LIPIcs.DISC.2023.42},
  annote =	{Keywords: Byzantine Agreement, Consensus, Optimistic-Pessimistic, Secure Multi-Party Computation}
}

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

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Brief Announcement: Scalable Agreement Protocols with Optimal Optimistic Efficiency

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