The security key is the same as the one you would use to connect with any wireless PC. If you do not have that then you are not allowed to use the system.
Now if you mean the mac address. You should be able to see that if you ask the device to scan for nearby wireless.
Be aware you can not normally get a repeater to work unless you have access to the main router to put in the mac of your repeater. Now if you really only have a single device you can make it work in client bridge mode. This only uses a single mac address so it looks no different than any other device. These used to be sold as gaming adapters to in effect convert the ethernet port on a game console to wifi. They are hard to find now but your device should have a client-bridge option.
Using a repeater to either extend the signal to another device via wireless or to hook multiple device up the main router must accept multiple mac address over the same encrypted path. This is normally a violations of the security so the routers normally require special configuration to work normally on the main router.