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# Brief Announcement: Multi-Threshold Asynchronous Reliable Broadcast and Consensus

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LIPIcs.DISC.2020.48.pdf
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• 3 pages

## Cite As

Martin Hirt, Ard Kastrati, and Chen-Da Liu-Zhang. Brief Announcement: Multi-Threshold Asynchronous Reliable Broadcast and Consensus. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 48:1-48:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.DISC.2020.48

## Abstract

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
##### Keywords
• byzantine agreement
• multi-threshold

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