Multi-Threshold Asynchronous Reliable Broadcast and Consensus

Authors Martin Hirt, Ard Kastrati, Chen-Da Liu-Zhang

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Author Details

Martin Hirt
  • Department of Computer Science, ETH Zürich, Switzerland
Ard Kastrati
  • Department of Information Technology and Electrical Engineering, ETH Zürich, Switzerland
Chen-Da Liu-Zhang
  • Department of Computer Science, ETH Zürich, Switzerland

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Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang. Multi-Threshold Asynchronous Reliable Broadcast and Consensus. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Classical protocols for reliable broadcast and consensus provide security guarantees as long as the number of corrupted parties f is bounded by a single given threshold t. If f > t, these protocols are completely deemed insecure. We consider the relaxed notion of multi-threshold reliable broadcast and consensus where validity, consistency and termination are guaranteed as long as f ≤ t_v, f ≤ t_c and f ≤ t_t respectively. For consensus, we consider both variants of (1-ε)-consensus and almost-surely terminating consensus, where termination is guaranteed with probability (1-ε) and 1, respectively. We give a very complete characterization for these primitives in the asynchronous setting and with no signatures: - Multi-threshold reliable broadcast is possible if and only if max{t_c,t_v} + 2t_t < n. - Multi-threshold almost-surely consensus is possible if max{t_c, t_v} + 2t_t < n, 2t_v + t_t < n and t_t < n/3. Assuming a global coin, it is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n. - Multi-threshold (1-ε)-consensus is possible if and only if max{t_c, t_v} + 2t_t < n and 2t_v + t_t < n.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic protocols
  • Theory of computation → Distributed algorithms
  • Security and privacy → Cryptography
  • broadcast
  • byzantine agreement
  • multi-threshold


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