[raphman]

Fair point. I was initially thinking about rainbow tables. Taking a hash and looking up associated passwords in a table feels like deriving to me - but I'm not a native speaker so I might have a wrong feeling here.

(It is obvious that one cannot directly derive the exact input - but one can derive potential inputs and then use other means to find the exact one.)

[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.