The scenario
You have an USB stick storage. You just want to use it only from your computer. It should be auto mounted from your computer and it should be available to all users of your computer before any login (Like network connection).
However, if any some one else decided, even you, to use it from another computer, this stick should not be mounted at all. It may be appeared as faulty or it should be formatted first.
The assignment of term specific machine
may be done by comparing hash value in a specific file on the system or using MAC address or any other way.