If you plan to create PL/SQL interfaces to libraries, only grant the EXECUTE privilege to the PL/SQL interface. Do not grant EXECUTE on the underlying library. You must have the EXECUTE privilege on a library to create the PL/SQL interface to it. However, users have this privilege implicitly on libraries that they create in their own schemas. Explicit grants of EXECUTE ON library_name are rarely required. Only make an explicit grant of these privileges to trusted users, and never to the PUBLIC role.