Researchers have discovered a series of theoretical attacks against Bitcoin's Nakamoto consensus; the most damaging ones are selfish mining, double-spending, and consistency delay attacks. These attacks have one common cause: block withholding. This paper proposes Crystal, which leverages quorum certificates to resist block withholding misbehavior. Crystal continuously elects committees from miners and requires each block to have a quorum certificate, i.e., a set of signatures issued by members of its committee. Consequently, an attacker has to publish its blocks to obtain quorum certificates, rendering block withholding impossible. To build Crystal, we design a novel two-round committee election in a Sybil-resistant, unpredictable and non-interactive way, and a reward mechanism to incentivize miners to follow the protocol. Our analysis and evaluations show that Crystal can significantly mitigate selfish mining and double-spending attacks. For example, in Bitcoin, an attacker with 30% of the total computation power will succeed in double-spending attacks with a probability of 15.6% to break the 6-confirmation rule; however, in Crystal, the success probability for the same attacker falls to 0.62%. We provide formal end-to-end safety proofs for Crystal, ensuring no unknown attacks will be introduced. To the best of our knowledge, Crystal is the first protocol that prevents selfish mining and double-spending attacks while providing safety proof.
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