Alan Is a Freshman in the Computer Science Department

Alan is a freshman in the computer science department. One of his professors has embarrassed him in class and then mocked him, saying that Alan will never be as good as she is with computers. In order to prove the professor wrong, Alan decides to break into the main computer at the Department of Defense and leave a note saying the professor is a spy. Alan indeed hacks into the computer and leaves the message. He designed the message to erase itself after 13 hours, leaving no trail and no damage to the computer. If Alan is discovered to be the hacker, has he committed a crime? Explain.