Frugal Byzantine Computing

Authors Marcos K. Aguilera, Naama Ben-David, Rachid Guerraoui, Dalia Papuc, Athanasios Xygkis, Igor Zablotchi

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Author Details

Marcos K. Aguilera
  • VMware Research, Palo Alto, CA, USA
Naama Ben-David
  • VMware Research, Palo Alto, CA, USA
Rachid Guerraoui
  • EPFL, Lausanne, Switzerland
Dalia Papuc
  • EPFL, Lausanne, Switzerland
Athanasios Xygkis
  • EPFL, Lausanne, Switzerland
Igor Zablotchi
  • MIT, Cambridge, MA, USA

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Marcos K. Aguilera, Naama Ben-David, Rachid Guerraoui, Dalia Papuc, Athanasios Xygkis, and Igor Zablotchi. Frugal Byzantine Computing. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Traditional techniques for handling Byzantine failures are expensive: digital signatures are too costly, while using 3f+1 replicas is uneconomical (f denotes the maximum number of Byzantine processes). We seek algorithms that reduce the number of replicas to 2f+1 and minimize the number of signatures. While the first goal can be achieved in the message-and-memory model, accomplishing the second goal simultaneously is challenging. We first address this challenge for the problem of broadcasting messages reliably. We study two variants of this problem, Consistent Broadcast and Reliable Broadcast, typically considered very close. Perhaps surprisingly, we establish a separation between them in terms of signatures required. In particular, we show that Consistent Broadcast requires at least 1 signature in some execution, while Reliable Broadcast requires O(n) signatures in some execution. We present matching upper bounds for both primitives within constant factors. We then turn to the problem of consensus and argue that this separation matters for solving consensus with Byzantine failures: we present a practical consensus algorithm that uses Consistent Broadcast as its main communication primitive. This algorithm works for n = 2f+1 and avoids signatures in the common case - properties that have not been simultaneously achieved previously. Overall, our work approaches Byzantine computing in a frugal manner and motivates the use of Consistent Broadcast - rather than Reliable Broadcast - as a key primitive for reaching agreement.

Subject Classification

ACM Subject Classification
  • Theory of computation → Concurrent algorithms
  • Theory of computation → Distributed algorithms
  • Theory of computation → Design and analysis of algorithms
  • Reliable Broadcast
  • Consistent Broadcast
  • Consensus
  • Byzantine Failure
  • Message-and-memory


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