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Researchers have discovered a series of theoretical attacks against Bitcoin'sNakamoto consensus; the most damaging ones are selfish mining, double-spending,and consistency delay attacks. These attacks have one common cause: blockwithholding. This paper proposes Crystal, which leverages quorum certificatesto resist block withholding misbehavior. Crystal continuously elects committeesfrom miners and requires each block to have a quorum certificate, i.e., a setof signatures issued by members of its committee. Consequently, an attacker hasto publish its blocks to obtain quorum certificates, rendering blockwithholding impossible. To build Crystal, we design a novel two-round committeeelection in a Sybil-resistant, unpredictable and non-interactive way, and areward mechanism to incentivize miners to follow the protocol. Our analysis andevaluations show that Crystal can significantly mitigate selfish mining anddouble-spending attacks. For example, in Bitcoin, an attacker with 30% of thetotal computation power will succeed in double-spending attacks with aprobability of 15.6% to break the 6-confirmation rule; however, in Crystal, thesuccess probability for the same attacker falls to 0.62%. We provide formalend-to-end safety proofs for Crystal, ensuring no unknown attacks will beintroduced. To the best of our knowledge, Crystal is the first protocol thatprevents selfish mining and double-spending attacks while providing safetyproof.

Crystal: Enhancing Blockchain Mining Transparency with Quorum Certificate