Can you extract domain names and usernames from the U2F devices? Like if someone wants to learn what sites he is visiting and his usernames?
In practice, no, the tokens are _way_ too dumb to remember anything like that. They're using an old cryptographic trick to appear much cleverer than they really are. During enrollment they present the server with a public key, and a magic cookie, both of which it stores. In subsequent authentication, the server sends them back the cookie, and some random data, which the token then signs to prove it still knows the pr…
This feels so much like cheating that I was sure it must be flawed, but I couldn't come up with any weakness.
I conviced myself that this is possible by considering the method of using a different permutation of the same key pair on each website and storing that permutation, encrypted, in a cookie.
Cryptography is awesome.