what is wrong about thinking

prbobability of attacker increases with time t that goes into PoW since they have more time to secretly mine their alternate blockchain ?

This refer to double spending. Can one think in these terms or is progress of finding a solution to pow to related to it.

Please enlighten.

  • update:also, how is probabilty and hash hashpower related – peter Jul 20 '18 at 14:54

Time only helps the attacker if they have more hashpower than all other miners together. That scenario is called a and discussed on numerous questions on this site. Such an attacker can essentially rewrite arbitrary lengths of history.

However, if the attacker only has minority hashrate, time works against them. The more time passes, the more likely is it that other miners advance the blockchain further than the attacker in the same time. Once the attacker falls behind, nobody will consider their chaintip when it is broadcast and the attack is failed.

  • thank you ok . but in white paper p=probility that an honest node finds the next block ... does that mean that p is also hash power ? What is the probability ? it links to hashpower also ? – peter Jul 21 '18 at 3:55
  • The probability of being the author of the next block corresponds to the relative portion of the total hashpower one contributes. With 10% of the hashpower, you should expect to find 1 out of 10 blocks. – Murch Jul 23 '18 at 15:57

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