From Partial to Global Asynchronous Reliable Broadcast

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\u2780] 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\u2700], Considine et al. [JC\u2705] and Raykov [ICALP\u2715], 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 $t 4$ even, is secure up to $t 4$ 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