I have two independent drupal-installations on the same server (one is the public area the other one is the private area). I want the (already registered) users to login to the private site from the public site. This shall be just a redirection, but before the authentication, because the user credentials are handled on the private installation. I imagine this as a kind of a tunnel.
I am using Drupal 6.22.
If the public site, and the private site are two sub-domain of the same domain, then you can use Bakery Single Sign-On System.
You can see it in action on the drupal.org sub-domains. When you need to log in to groups.drupal.org, you are really logging in to drupal.org.