How to disable "From email address" for unauthorized users?
You can try following:


Go to Administer-> Customize data and Screens-> Navigation Menu and  select Mailing.
From mailing option, do right click and edit on 'From Email Address'.
In the next window, you can choose permission to that particular menu under 'Mailing'.
After choosing permission for menu, assign that permission to the role you want.


With this you can give permission to single submenu. 

If you want restrict unauthorized user, simply do not assign the permission to anonymous user