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.
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