You could probably use jquery from your master page to append a link, you would need to come up with a jquery selector that is unique to the login page by inspecting the rendered source you can figure something out. Probably something along the lines of
$('.login div.modulecontent').append('<a href=\"http://yoururltoyourpdf.pdf\" onclick=\"window.open(this.href,'_blank');return false;\">Your Link Text</a>');
This is just concept I have not tested it.
Hope it helps,
Joe