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alethiophile comments on Singularity Institute now accepts donations via Bitcoin - Less Wrong
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I am a bit confused. Why would this process need to be continually re-done? Once you have generated all the hashes of numbers less than 256 bits long, then you instantly (up to the speed of accessing the database entry) know a short preimage for every hash value.
That's not the idea. The computational problem is simply a proof of work--you create a specific, verifiable string, with a changeable component greater than 256 bits, then hash that string using incrementing values until you find a SHAsum less than a certain value. Knowing a random, short preimage for each possible hash doesn't help you there, because those will not allow you to create a verifiable string with the correct hash.