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Bitcoin uses a problem similar to that as a proof of work, although it uses SHA256 (actually SHA256 twice in a specified fashion), and you're modifying a small part of a larger message. With Bitcoin, you're trying to find a message which hashes to a value less than a specified target, which is expressed as a difficulty level. The higher the difficulty, the ...


As far as we know, SHA512 acts like a random function. So, the only way we know to find a preimage whose hash starts with 0x12345678, is to go through distinct preimages, and hash each one until we find one that starts with 0x12345678. If the output of SHA512 is equidistributed (and we have no reason to believe it isn't), then the probability of any hash ...

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