Fault tolerance of a blockchain is often characterized by the fraction $f$ of ``adversarial power'' that it can tolerate in the system. Despite the fast progress in blockchain designs in recent years, existing blockchain systems can still only tolerate $f$ below $\frac{1}{2}$. Can practically usable blockchains tolerate a malicious majority, i.e., $f \ge \frac{1}{2}$? This work presents a positive answer to this question. We first note that the well-known impossibility of {\em byzantine consensus} under $f \ge \frac{1}{2}$ does not carry over to blockchains. To tolerate $f \ge \frac{1}{2}$, we use {\em byzantine broadcast}, instead of byzantine consensus, as the core of the blockchain. A major obstacle in doing so, however, is that the resulting blockchain may have extremely low throughput. To overcome this central technical challenge, we propose a novel byzantine broadcast protocol OverlayBB, that can tolerate $f \ge \frac{1}{2}$ while achieving good throughput. Using OverlayBB as the core, we present the design, implementation, and evaluation of a novel Proof-of-Stake blockchain called BCube. BCube can tolerate a malicious majority, while achieving practically usable transaction throughput and confirmation latency in our experiments with $10000$ nodes and under $f = 0.7$. To our knowledge, BCube is the first blockchain that can achieve such properties.

翻译：块链的不透明容忍度通常以其在系统中能够容忍的“ 对抗性电量” 的零用金为特征。 尽管近年来块链设计取得了快速进展, 现有的块链系统仍然只能容忍低于$\\f{1\\\2}$的美元。 实际可用的块链能够容忍恶意多数, 即, $f\ ge\ ge\ flac{1\\2}? 这项工作是对这一问题的一个积极答案。 我们首先注意到, 在 美元\ ge\ fredi 下, “ 对抗性电量” 是众所周知的。 在 美元\ fref\ flac\ x2} 下, 众所周知, 以“ 对抗性电量 ” 的“ 平面电量 ” 无法传递。 要容忍$ge $\ frefge $ $\ fraxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx/xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx