Dynamic Probabilistic Reliable Broadcast

TL;DR

This paper proposes a solution in which every broadcast message is validated by a small set of witnesses, which allows us to maintain low latency and small communication complexity, and exhibits significant scalability gains over state-of-the-art protocols.

Abstract

Byzantine reliable broadcast is a fundamental primitive in distributed systems that allows a set of processes to agree on a message broadcast by a dedicated process, even when some of them are malicious (Byzantine). It guarantees that no two correct processes deliver different messages, and if a message is delivered by a correct process, every correct process eventually delivers one. Byzantine reliable broadcast protocols are known to scale poorly, as they require $Ω(n^2)$ message exchanges, where $n$ is the number of system members. The quadratic cost can be explained by the inherent need for every process to relay a message to every other process. In this paper, we explore ways to overcome this limitation, by casting the problem to the probabilistic setting. We propose a solution in which every broadcast message is validated by a small set of witnesses, which allows us to maintain low latency and small communication complexity. In order to tolerate the slow adaptive adversary, we dynamically select the witnesses through a novel stream-local hash function: given a stream of inputs, it generates a stream of output hashed values that adapts to small deviations of the inputs. Our performance analysis shows that the proposed solution exhibits significant scalability gains over state-of-the-art protocols.

Figures (5)

• Figure 1: Illustration of how stream local hashing of similar histories ($S$ and $\hat{S}$) results in similar witness set selections ($W$ and $\hat{W}$).
• Figure 2: Average number of instances for gathering according to expected witness set size. The parameters used are: $n=1024$, $b = 4$, $r = 2^{10}$, $k = 0.45w$. Each curve is for distinct $t$, the fraction of malicious nodes.
• Figure 3:
• Figure 4: Simulations (thick line) and simplified analysis (dashed line). On the left graph: $r = 2^{10}$. On the right graph: $b = 8$. In both graphs $t = 0.25$, $c = 2$ and $s = 0.5$.
• Figure 5: Liveness and Consistency failure times. The parameters used are: $n=1024$, $b = 4$, $r = 2^{10}$, $k = 0.45w$ and $t = 0.25$.

Theorems & Definitions (14)

• Definition 1: Long-lived Probabilistic Reliable Broadcast
• Theorem 2
• Theorem 3: Locality
• Theorem 4: Witness Inclusion
• Theorem 5: Unpredictability
• Proposition 6
• Proposition 7
• Proposition 8
• Theorem 4: Witness Inclusion
• Theorem 5: Unpredictability