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As far as I understand, an attacker (in the role of a malicious miner) controlling a large portion of the current hash power could replace previously accepted blocks with alternatives.

But, what does that mean? He could

  • Collect the block reward
  • Add previously unconfirmed transactions, making them confirmed
  • Omit formerly confirmed transactions

But what would an attacker gain with this?

  • Block rewards are easier collected with real mining
  • Unconfirmed transactions may eventually confirm anyway
  • Omitted transactions may confirm just a while later anyway, too

So what's the danger with majority attacks?

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  • Besides the technical posibilities to do a 51% attack, I would like to add, that it is nearly impossible from a complexity point of view. The required amount of mining equipment to achieve current hashrate is roughly 800.000 ANTMINER S9. They would "eat" 1000 MW of power (a nuclear power centre, or 500 wind power systems of the 2MW class). So this attack seems a very poor approach. On the otherhand one can think about miner centralization and "buy them". The amount of money required would have to be in the billion Euros (maybe half of bitcoin market value?). Thinkable, but not that easy.
    – pebwindkraft
    Dec 24 '17 at 11:00
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An attacker controlling more than half of the mining power could do a few things. For example.

  1. They could declare certain transactions as invalid. By refusing to include them in their blocks and refusing to build on any block that includes them the unwanted transactions would see any confirmations they picked up quickly reversed. Someone trying to make money could use this to set minimum transaction fees. A government trying to regulate bitcoin could allow only addresses registered with the government.
  2. They could collect all the mining rewards by refusing to build on anyone else's blocks, since the total mining rewards are roughly fixed this would get them more bitcoins than just taking their fair share of mining rewards.
  3. They could spend bitcoins to get something non-bitcoin in exchange and then later reverse those transactions leaving the people they exchanged with out of pocket.

If the attackers aim is to make money these things are probably a bad idea. They would likely destroy the value of bitcoin and destroy the attackers profits

OTOH if the attackers goal is to destroy or subvert bitcoin these things may be more worth doing.

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So what's the danger with majority attacks?

The danger is more that such an attacker would be able to censor transactions and dictate what valid transactions are and are not allowed by refusing to mine certain transactions. With sufficient hashrate, the attacker could refuse to build upon anyone else's blocks, and with a majority hashrate, he could then make his blockchain the accepted one because it would have more total work than any other chain. This would mean that transactions which the attacker does not like would never be confirmed as they never make it into a block on the main chain. Other than that, there isn't much that an attacker can do with majority hashrate, but it still would be a problem.

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