Any authentication is one-to-one. The server authenticates to me, by first knowing who I am (my 'username' not a password), then using a scheme we agreed upon (our shared pair of private/public keys would be fine) to verify electronically that my machine belongs to me i.e. has the right keys.

So we are both authenticated to one another. Except now, we're using sophisticated passwords and Digital Computer Logic to work them out. Instead of my fallible wetware.