Limiting finger lookup access on Linux

I have some linux machines that I have configured for student access. We are authenticating against our OpenLDAP tree and limiting which users have access via an LDAP groupOfNames. This is all working perfectly.

This is the problem I am having. Any user with access to the system can run the /usr/bin/finger command and do a name search against our entire LDAP tree. I would like to limit the info available via finger to just the users that have access to any particular machine. How can this be controlled?

-Rex