When I buy an U2F device, say a Yubikey smart-card, does the vendor hardcode on it a private key that will be later used in a challenge-response mechanism by the user, or do they only put in there some kind of 'seed', which is later used to create a private key when I plug the device in my computer?
In the first case, how likely is a scenario where vendor is compromised and leaks my private key? in the second, is it mathematically possible known the seed to reconstruct my private key?
If instead I completely misunderstood how it works, could you please correct me?