# Enhancing Bitcoin Security and Performance with Strong Consistency via Collective Signing

arXiv: https://arxiv.org/abs/1602.06997 · HTML: https://mlsanity.com/paper/1602.06997/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2016.

## Built on by (most cited first, 4 of 4)

- [GradientCoin: A Peer-to-Peer Decentralized Large Language Models](https://mlsanity.com/paper/2308.10502/) (2023)
- [MAD-Spear: A Conformity-Driven Prompt Injection Attack on Multi-Agent Debate Systems](https://mlsanity.com/paper/2507.13038/) (2025)
- [AnoFel: Supporting Anonymity for Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2306.06825/) (2023)
- [A Survey on Blockchain-Based Federated Learning and Data Privacy](https://mlsanity.com/paper/2306.17338/) (2023)

## Abstract (arXiv)

While showing great promise, Bitcoin requires users to wait tens of minutes for transactions to commit, and even then, offering only probabilistic guarantees. This paper introduces ByzCoin, a novel Byzantine consensus protocol that leverages scalable collective signing to commit Bitcoin transactions irreversibly within seconds. ByzCoin achieves Byzantine consensus while preserving Bitcoin's open membership by dynamically forming hash power-proportionate consensus groups that represent recently-successful block miners. ByzCoin employs communication trees to optimize transaction commitment and verification under normal operation while guaranteeing safety and liveness under Byzantine faults, up to a near-optimal tolerance of f faulty group members among 3f + 2 total. ByzCoin mitigates double spending and selfish mining attacks by producing collectively signed transaction blocks within one minute of transaction submission. Tree-structured communication further reduces this latency to less than 30 seconds. Due to these optimizations, ByzCoin achieves a throughput higher than PayPal currently handles, with a confirmation latency of 15-20 seconds.