Can a Password be Derived from a AES key?
Given an AES key, lets say an AES-256 key which is derived from a user password, is there any way to analyze the key and reverse engineer the password used to generate the key?


This is really the same problem as password cracking, where the simple strategy of trying statistically likely passwords at very high speed with specialized, massively parallel hardware (e.g., GPUs) has proven to be very fruitful.  This doesn't involve any sort of cryptanalytic attack to reverse the key derivation function, rather just relying on (a) the predictability of real-world passwords and (b) the fitness of GPUs for this sort of task.

If you're not familiar with this topic, this article and the enclosed video are a good primer.