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Mobile Networks use symmetric keys for mutual authentication. You need the same key both in SIM and the carriers database.

What I guess you mean is, you buy an inactive SIM from Vodafone (which has Vodafone-known keys on it), and then you’re telling Vodafone to use that card.

By „bring your SIM“ I thought of something non-branded and was surprised.

Essentially that is what’s happening with eSIM, hence the need for the provisioning step that also makes transferring hard.