Yeah, a general solution wouldn't be useful in the wild against keys that are never used in the probabilistic approach i am thinking of, observations of cipher text are needed (which isn't unbounded).
Assuming hash(str) has polynomial time, the nondeterministic algorithm above is clearly polynomial as well. Here `choice` is not a function, it is an elementary nondeterministic operation, one which evaluates the given function on each value in the input variable in O(1). AllStrings is the set of all strings, maybe limited to some max length if desired (otherwise, matchingPasswords will be an infinite set itself).
As far as it is known, there is no way to replace this with any sampling method that would take polynomial time. Of course, this is not proven, it is a related problem known as BPP=NP. BPP is the class of problems for which Bounded-error Probabilistic algorithms with Polynomial time complexity exist.
As far as it is known, there is no way to replace this with any sampling method that would take polynomial time. Of course, this is not proven, it is a related problem known as BPP=NP. BPP is the class of problems for which Bounded-error Probabilistic algorithms with Polynomial time complexity exist.