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Hierarchical Consensus: Scalability Through Optimism and Weak Liveness

Authors Pedro Antonino, Antoine Durand, A. W. Roscoe

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Subject Classification

ACM Subject Classification
  • Networks → Network protocol design
  • Theory of computation → Distributed algorithms
Keywords
  • Hierarchical
  • Handover
  • Justifiability
  • Consensus
  • Distributed Systems
  • Blockchain

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Abstract

Scalability is a central concern of Byzantine Fault Tolerant (BFT) distributed protocols. The ubiquitous approach to work around the well-known Dolev-Reischuk Ω(n²) communication complexity lower bound is to use a random selection process to draw a hopefully small committee from a population of agents to run the communication-heavy protocol. We propose a notion of hierarchical consensus that combines two sub-protocols: an optimistic primary sub-protocol that can tolerate less than 1/2 failures and a fallback secondary protocol that can tolerate less than 1/3 failures; we achieve the higher failure threshold by requiring a weaker notion of liveness for the primary. This distinction between the level of fault tolerance between primary and secondary is reflected in the size of committees implementing these protocols. For a population of agents with close to 2/3 of honest agents, we need to select a committee with hundreds of agents to reach the level of tolerance expected for the primary, whereas we need thousands to reach the level expected for the secondary with a very small probability of error ε. Our hierarchical construct is such that if the primary comes to a decision, it can simply propagate it to the secondary protocol, so it does not need to properly engage in an agreement protocol independently. Our architecture is flexible and allows us to use our technique for most protocols that are based on random sampling. By studying hierarchical protocols, we discovered new theoretical results of independent interest. Specifically, the ability to handover from a primary protocol requires a new Justifiability property that allows agents to pre-decide on a value, such that if the protocol decides, it must be on that pre-decided value.

Cite As Get BibTex

Pedro Antonino, Antoine Durand, and A. W. Roscoe. Hierarchical Consensus: Scalability Through Optimism and Weak Liveness. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.6

Author Details

Pedro Antonino
  • The Blockhouse Technology Ltd., Oxford, UK
Antoine Durand
  • The Blockhouse Technology Ltd., Oxford, UK
A. W. Roscoe
  • The Blockhouse Technology Ltd., Oxford, UK
  • University College Oxford Blockchain Research Centre, UK

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