Apparently I don't understand how hotel card keys work. I always assumed that keys were manufactured with a random UUID inside them, and then when you checked in, a random card was attached to your room and given to you.
When you try to open a door, it compares your card's ID to the room database to see if the door should open.
Is that... not how it works? Because that seems simpler than anything that involves encryption, or actually writing shit to the card.