最优自适应多值拜占庭共识
Optimal Adaptive Multi-Valued Byzantine Agreement
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中文总结 AI 辅助
该研究在Constantinescu等人的二进制拜占庭共识协议基础上，扩展出多值拜占庭共识协议，在同步、部分同步、异步场景下达到最优弹性，优化了复杂度与延迟，适配大规模分布式系统需求。
中文摘要 AI 辅助
在拜占庭共识（Byzantine Agreement，BA）中，共有n个参与方，其中t个可能是拜占庭节点，它们运行分布式协议以就共同的有效输入达成一致。传统上，这些协议具有线性延迟和二次消息复杂度，使其在大规模场景下不实用。Constantinescu、Dufay、Paramonov和Wattenhofer在近期工作中考虑了实际拜占庭节点数量f ≤ t，致力于解耦复杂度对n和t的依赖，得到了消息复杂度为$\tilde{\theta}(n + t·f)$、轮复杂度为$\tilde{\theta}(f)$的BA协议，但他们的结果严格局限于二进制值的共识。我们利用其工作提供的框架并结合新技术，将这些结果扩展到L位值的BA。设κ为安全参数，且在同步设置中达到最优弹性（t < n/2），否则（异步等场景）为t < n/3，我们得到以下结果：1. 同步场景下，确定性协议的位复杂度为$\theta(n·(L + f·κ))$，轮复杂度为$\theta(f + \text{log }n)$；2. 同步和部分同步场景下，确定性协议的位复杂度为$\tilde{\theta}(n·κ + t·(L + f·κ))$，轮复杂度为$\theta(f)$；3. 异步场景下，协议的期望位复杂度为$\tilde{\theta}(n·κ + t·(L + t·κ))$，期望延迟为$\theta(1)$。
英文摘要
In Byzantine Agreement (BA), $n$ parties, out of which $t$ can be Byzantine, run a distributed protocol to agree on a common valid input. Traditionally, these protocols have a linear latency and quadratic message complexity, making them impractical at a large scale. In their recent work, Constantinescu, Dufay, Paramonov, and Wattenhofer consider the actual number of byzantine parties $f \leq t$ and work toward decoupling the dependency on $n$ and $t$ in the complexity. They obtain a BA protocol with $\tilde{\mathcal{O}}(n + t\cdot f)$ message complexity and $\tilde{\mathcal{O}}(f)$ round complexity. However, their results are strictly limited to agreement on a binary value. Using the framework given by their work along with novel techniques, we extend these results for BA on an $L$-bit value. With $κ$ being a security parameter, and with optimal resiliency ($t < n/2$ in the synchronous setting or $t < n/3$ otherwise), we obtain: - In synchrony, a deterministic protocol with $\mathcal{O}(n\cdot (L + f \cdot κ))$ bit complexity and $\mathcal{O}(f + \log n)$ round complexity. - In synchrony and partial synchrony, deterministic protocols with $\tilde{\mathcal{O}}(n \cdot κ+ t\cdot (L + f \cdot κ))$ bit complexity and $\mathcal{O}(f)$ round complexity. - In asynchrony, a protocol with $\tilde{\mathcal{O}}(n \cdot κ+ t\cdot(L + t \cdot κ))$ expected bit complexity and expected $\mathcal{O}(1)$ latency.
