And of course it's also useful for providing secure authentication.

In both cases the strength of the system is that it provides extremely good security and authentication because you're able to publish the public key.

You buy that once, and you own it, and they provide free authentication forever.

That is to both provide confidentiality and authentication.

Google provides optional free two-factor authentication for greater account security.

So it really does provide good authentication and integrity checking for that.

As such, the telephone switch, and therefore the operating entity, must also be trusted to provide secure authentication.

The ability to reset the password without providing authentication apparently only works for the current user.

Rather, it provides authentication, as only a single person (theoretically) has access to the private key.

It's about the integrity of the system's, the Internet's ability to provide authentication of a virtual person.