Can linux or other unix create a file that no user, including root, can modify unless they have the secret key? By "have the secret key" I mean they are using some crypto scheme.

Here's a scenario if you aren't already downvoting:

Bob encrypts something about file /foo (maybe inode?) using secret key K

Alice tries "sudo rm /foo" and gets permission denied, so she decrypts something about file /foo using secret key K and then "sudo rm /foo" succeeds.