This thought randomly popped into my head and I have not been able to find a clear, defined answer for it. 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?
I understand if the key has been revealed and is known to an attacker they already have what they need, but this is a theoretical. Alternatively, a hacker may leverage a weakly protected system, stealing the key for a particular user from that system, reverse engineer the password then hope the user used the same password on a more secure system that the hackers primary goal is to access that.
I apologize if this is an obvious question, I am a software developer trying to break into the security field and attempting to develop my understanding of cryptographic principles.