Crystal: Enhancing Blockchain Mining Transparency With Quorum Certificate
Bibliographic record
Abstract
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".