For U2F I don't believe that's the case for most devices.
Yubikey outlines their method here[1]. They generate a different keypair for each website public key and have the server store an encrypted and authenticated copy of the private key using a single on-device key. So baring breaking the underlying primitives the server will only have a site-specific public key and a site-specific encrypted blob.
Yubikey outlines their method here[1]. They generate a different keypair for each website public key and have the server store an encrypted and authenticated copy of the private key using a single on-device key. So baring breaking the underlying primitives the server will only have a site-specific public key and a site-specific encrypted blob.
[1]: https://developers.yubico.com/U2F/Protocol_details/Key_gener...