Is there any loss of privacy while using 2 Factor authentication?
If you use Google Authenticator on an android phone (where essentially you have linked your google id), to authenticate the login of a third party website, can google link your google id with the credentials of the third party website?
from google support
"Google sends a random code to third-party sites to enable you to sign in to these sites with your Google Account. This code doesn't reveal any personal information. Also, the security of your Google Account will not be compromised by signing in to other sites with your account."