I'm currently building a web application and would like to encrypt all data on the back-end. I was thinking of using the AES-256 encryption but wasn't sure how safe it was. I did that math and felt safe.
I took this model to a professor at my college, who is a cyber security expert, and he seemed to have quite a different take. He told me there are only two encryption schemes that he knows of that cannot be broken, and AES is not one of them. He said sure, put it in, but just know that there are people out there who can crack it.
I Googled everything I could about the AES and it being cracked, and the only information I could find was this paper: Distinguisher and Related-Key Attack on the Full AES-256 (Extended Version). Sure it says the AES has been cracked but is still has a practical use, right? I believe it is $2^{231}$ instead of $2^{256}$.
So what gives? Is it practically secure to use or not? Does he just know something that most people don't? If my web application database credentials are somehow exposed, and a hacker gets the raw encrypted data, how can I ensure he won't be able to decrypt it within his lifetime?