'Bitcoin Byzantine Fault Tolerance: Is 51% Really Sufficient?
In the Bitcoin Whitepaper Nakamoto mentions that as long as a majority of the network's computing power is controlled by honest nodes, those nodes will continue to outpace attackers and generate the longest chain. So it seems like the Bitcoin network is safe if the proportion of malicious nodes is below half, assuming all nodes have equal computing power such that n >= 2f + 1 is sufficient for consensus. However, we also have the n >= 3f + 1 lower bound result which says we need at least 3f+1 total nodes to reach consensus with f Byzantine failure nodes. This seems like a contradiction. Might an attacker be able to thwart the Bitcoin network from reaching consensus if they control slightly more than 1/3 of the nodes? Or does the n >= 3f + 1 lower bound not apply to Bitcoin? Or something else?
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