passing username + password to another site

I have a Drupal based CMS and a Gallery based IMS on the same server. I want users to be able to go from one to the other without having to login.

Maybe it's so simple no-one has asked - can I get hold of the username and password (in clear) and pass them from the Drupal site in the link to the Gallery site?

For instance for the link from Drupal, maybe use http:// mygallerysite?username=fred&password=fredspassword
but I need to get 'fred' and 'fredspassword' from somewhere.

I guess it might involve cookies?

Help would be very much appreciated...