**Multi-Threshold Asynchronous Reliable Broadcast and Consensus**

*Martin Hirt and Ard Kastrati and Chen-Da Liu-Zhang*

**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 $f \le t_v$, $f \le t_c$ and $f \le t_t$ respectively. For consensus, we consider both variants of $(1-\epsilon)$-consensus and \emph{almost-surely terminating} consensus, where termination is guaranteed with probability $(1-\epsilon)$ 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 $(1-\epsilon)$-consensus is possible if and only if $\max\{t_c, t_v\} + 2t_t < n$ and $2t_v + t_t < n$.

**Category / Keywords: **cryptographic protocols / reliable broadcast, consensus, byzantine agreement, multi-threshold

**Date: **received 5 Aug 2020

**Contact author: **lichen at inf ethz ch

**Available format(s): **PDF | BibTeX Citation

**Version: **20200811:113741 (All versions of this report)

**Short URL: **ia.cr/2020/958

[ Cryptology ePrint archive ]