This is a quote from the book "Bitcoin: A Peer-to-Peer Electronic Cash System" by Satoshi Nakamoto
...rk effort invested in it. If a majority of CPU power is controlled by honest nodes, the honest chain will grow the fastest and outpace any competing chains. To modify a past block, an attacker w
ould have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the honest nodes. We will show later that the probability of a slower atta
cker catching up diminishes exponentially as subsequent blocks are added.
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To compensate for increasing hardware speed and varying interest in running nodes over time, the proof-of-w...