Since multiple values can result in the same hash, couldn’t an attacker try to find a way of increasing his balance in a way that the checksum of the changed block remains the same (so that any proofs-of-work are still valid) and then propagate the change into the network without peers noticing it?

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Sure, he can try. But the algorithms Bitcoin uses were specifically chosen to make this attack completely impractical. It would be trillions of times easier to just buy the Bitcoins.

  • And suppose he could come up with such a block (he can't, but for arguments sake). How is he going to give that block to others? Noone is going to replace a block that's been on their harddisks for years with a new one. He could only pollute the blockchain of some random new user downloading a fresh copy. Surely an awkward situation for a few individuals, but hardly a significant fork.
    – Jannes
    Dec 24, 2013 at 0:40

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