Comment by Cpoll

To me, "deriving from x" means performing a mathematical function operating on input x. By my own definition, I suppose a rainbow table lookup is a derivation, but I wouldn't consider actually computing the table to be one. Hash-cracking is more like guess-and-check than mathematical decoding; the hash to be cracked is just a verifier and not an input, which is why I make the (admittedly pedantic) distinction.