License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2020.6
URN: urn:nbn:de:0030-drops-134917
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Hirt, Martin ; Kastrati, Ard ; Liu-Zhang, Chen-Da

Multi-Threshold Asynchronous Reliable Broadcast and Consensus

LIPIcs-OPODIS-2020-6.pdf (0.5 MB)


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.

BibTeX - Entry

  author =	{Martin Hirt and Ard Kastrati and Chen-Da Liu-Zhang},
  title =	{{Multi-Threshold Asynchronous Reliable Broadcast and Consensus}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Quentin Bramas and Rotem Oshman and Paolo Romano},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-134917},
  doi =		{10.4230/LIPIcs.OPODIS.2020.6},
  annote =	{Keywords: broadcast, byzantine agreement, multi-threshold}

Keywords: broadcast, byzantine agreement, multi-threshold
Collection: 24th International Conference on Principles of Distributed Systems (OPODIS 2020)
Issue Date: 2021
Date of publication: 25.01.2021

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