### From Partial to Global Asynchronous Reliable Broadcast

Diana Ghinea, Martin Hirt, and Chen-Da Liu-Zhang

##### Abstract

Broadcast is a fundamental primitive in distributed computing. It allows a sender to consistently distribute a message among $n$ recipients. The seminal result of Pease et al. [JACM'80] shows that in a complete network of synchronous bilateral channels, broadcast is achievable if and only if the number of corruptions is bounded by $t < n/3$. To overcome this bound, a fascinating line of works, Fitzi and Maurer [STOC'00], Considine et al. [JC'05] and Raykov [ICALP'15], proposed strengthening the communication network by assuming partial synchronous broadcast channels, which guarantee consistency among a subset of recipients. We extend this line of research to the asynchronous setting. We consider reliable broadcast protocols assuming a communication network which provides each subset of $b$ parties with reliable broadcast channels. A natural question is to investigate the trade-off between the size $b$ and the corruption threshold $t$. We answer this question by showing feasibility and impossibility results: 1) A reliable broadcast protocol that: For $3 \le b \le 4$, is secure up to $t < n/2$ corruptions; For $b > 4$ even, is secure up to $t < \left(\frac{b-4}{b-2} n + \frac{8}{b-2}\right)$ corruptions; For $b > 4$ odd, is secure up to $t < \left(\frac{b-3}{b-1} n + \frac{6}{b-1}\right)$ corruptions. 2) A nonstop reliable broadcast, where parties are guaranteed to obtain output as in reliable broadcast but may need to run forever, secure up to $t < \frac{b-1}{b+1} n$ corruptions. 3) There is no protocol for (nonstop) reliable broadcast secure up to $t \ge \frac{b-1}{b+1} n$ corruptions, implying that the reliable broadcast protocol is asymptotically optimal, and the nonstop reliable broadcast protocol is optimal.

Available format(s)
Publication info
Published elsewhere. DISC'20
Keywords
Contact author(s)
lichen @ inf ethz ch
History
Short URL
https://ia.cr/2020/963

CC BY

BibTeX

@misc{cryptoeprint:2020/963,
author = {Diana Ghinea and Martin Hirt and Chen-Da Liu-Zhang},
title = {From Partial to Global Asynchronous Reliable Broadcast},
howpublished = {Cryptology ePrint Archive, Paper 2020/963},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/963}},
url = {https://eprint.iacr.org/2020/963}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.