I'm not sure but if the Linux system you are moving the thumb drive too isn't running gnome the key may not work automatically.
Ensure your 'other' desktop has the following packages.
sudo apt-get install cryptsetup
See http://www.howtogeek.com/115955/how-to-quickly-encrypt-removable-storage-devices-with-ubuntu/ for further info.
The official Ubuntu page is https://help.ubuntu.com/community/EncryptedFilesystemsOnRemovableStorage
Where you also need to install the gnome disk utility, if you are connecting with gnome.
Looking at the 'expert' section you can use
dmesg | tail -20
To confirm that the disk is being correctly recognised.
I would recommend reading the official help page if you continue to have problems. Otherwise post your dmesg output into your question, and drop a comment to this answer if you need more help.
Reading to the end of the help page if the username on the 'other' system is not the same as on your 'main' one you may need to ensure that the username and group of /media/disk is correctly set. See the very bottom of the Ubuntu help page for more info.
If your other system isn't runny gnome by default head to the Debian help page http://www.hermann-uwe.de/blog/howto-disk-encryption-with-dm-crypt-luks-and-debian which from a quick scan should be desktop agnostic. Note however it is more command line oriented, so you may need to 'be brave' and not panic.
As I say post a comment if yo get problems.
Dave.