## From Partial to Global Asynchronous Reliable Broadcast

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

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:

-A reliable broadcast protocol that 1) For $3 \le b \le 4$, is secure up to $t < n/2$ corruptions; 2) For $b > 4$ even, is secure up to $t < \left(\frac{b-4}{b-2} n + \frac{8}{b-2}\right)$ corruptions; 3) For $b > 4$ odd, is secure up to $t < \left(\frac{b-3}{b-1} n + \frac{6}{b-1}\right)$ corruptions.

-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.

-There is no protocol for (nonstop) reliable broadcast secure up to $t \ge \frac{b-1}{b+1} n$ corruptions, implying that our reliable broadcast protocol is asymptotically optimal, and the nonstop version is optimal.

## BibTeX Citation

@inproceedings{GhHiLi20, author = {Diana Ghinea and Martin Hirt and Chen-Da Liu Zhang}, title = {From Partial to Global Asynchronous Reliable Broadcast}, booktitle = {International Symposium on Distributed Computing --- DISC 2020}, year = {2020}, month = {10}, }