[russum]

>>The keys are (I'm guessing) just stored in the SIM card

They're not. They keys (and many other things) are stored in "carrier settings" that your provider pushes to your smartphone. In the past we had to set things up like APN & etc manually for the internet to work but not anymore with the settings being pushed automatically (if the provider supports it).

On iOS you can view the current version of pushed settings by seeing the Settings > General > About -> Carrier option.

"Carrier settings updates are small files that can include updates from Apple and your carrier to carrier-related settings, such as network, calling, cellular data, messaging, personal hotspot, and voicemail settings". [1]

[1] https://support.apple.com/en-us/HT201270

[vegardx]

Ah, even cooler! What I liked about it was how transparent the whole thing was for me. I didn't have to do anything, it just sort of worked.