拜占庭因果可靠广播（BCRB）与常数大小消息元数据

中文摘要 AI 辅助

异步拜占庭可靠广播（BRB）是一种基本原语，保证在存在拜占庭故障的分布式系统中的一致性和有效性，但它缺乏排序保证。在本文中，我们研究拜占庭因果可靠广播（BCRB），它在BRB基础上强制执行因果消息排序。我们提出了一种新颖的BCRB协议，将因果排序与BRB层解耦，实现了常数大小$\mathcal{O}(1)$的消息元数据开销和$\mathcal{O}(n^2)$的通信字复杂度，而现有协议的通信字复杂度为$\mathcal{O}(n^3)$；这里$n$是进程数。我们提出了协议的两种变体：一种使用阈值加密方案和序列门控的加密版本，以及其非加密版本。在加密版本中，发送者立即广播密文，解密份额被搭载在带外确认（ACK）上，防止提前解密和抢跑。在两种版本中，因果安全性都是概率性实现的。我们使用独立指数链路延迟分布下的随机变量路径分析来评估因果安全违规的概率。我们证明两种变体都满足活性，且弱安全违规的概率以$\mathcal{O}(f^{-3}\cdot\ln^3 f)$为界，其中$f$是拜占庭进程数量的上界，且$f < n/3$和$f=\mathcal{O}(n)$。此外，对于加密版本，我们证明强安全违规的概率以$\mathcal{O}(f^{-1} \cdot \ln^2 f)$为界。我们还展示了如何修改我们的两种协议，以保证100%的弱安全性，同时保持$\mathcal{O}(1)$的消息空间开销，但消息数为$\mathcal{O}(n^3)$，通信字复杂度为$\mathcal{O}(n^3)$。

英文摘要

Asynchronous Byzantine Reliable Broadcast (BRB) is a fundamental primitive that guarantees agreement and validity in distributed systems subject to Byzantine faults, but it lacks ordering guarantees. In this paper, we address Byzantine Causal Reliable Broadcast (BCRB), which builds on BRB to enforce causal message ordering. We present a novel BCRB protocol that decouples causal ordering from the BRB layer, achieving constant-size $\mathcal{O}(1)$ message metadata overhead and $\mathcal{O}(n^2)$ communication word complexity as against $\mathcal{O}(n^3)$ communication word complexity of existing protocols; here $n$ is the number of processes. We present two variants of our protocol: a cryptographic version using a threshold encryption scheme and sequence gating, and its non-cryptographic version. In the cryptographic version, senders broadcast ciphertexts immediately, and decryption shares are piggybacked on out-of-band ACKs, preventing early decryption and front-running. In both versions, causal safety is achieved probabilistically. We evaluate the probability of causal safety violations using a random variable path analysis under independent exponential link delay distributions. We show that both variants satisfy liveness and the probability of weak safety violation is bounded by $\mathcal{O}(f^{-3}\cdot\ln^3 f)$, where $f$ is the upper bound on the number of Byzantine processes, and $f < n/3$ and $f=\mathcal{O}(n)$. Further, for the crypto version, we show that the probability of strong safety violation is bounded by $\mathcal{O}(f^{-1} \cdot \ln^2 f)$. We also show how to modify our two protocols to guarantee 100\% weak safety keeping $\mathcal{O}(1)$ message space overhead but with $\mathcal{O}(n^3)$ messages and $\mathcal{O}(n^3)$ communication word complexity.

发表机构

• University of Illinois Chicago（伊利诺伊大学芝加哥分校）

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