GnuPG - How can Ubuntu encrypt messages automatically

GnuPG - How can Ubuntu encrypt messages automatically

I am running a 12.04LTS Ubuntu Server (Linux myserver 3.2.0-52-generic-pae
#78-Ubuntu SMP Fri Jul 26 16:43:19 UTC 2013 i686 athlon i386 GNU/Linux)
with a FQDN and an Exim4 Mailserver. User Alice has UID1000 and is getting
the messages from root, messages send to root by local services and is
getting messages from various cron jobs executed by root and Alice. I have
also generated a GnuPG keypair for alice@myFQDN.net.
What i want to do, is that the system encrypts the messages generated
locally "automatically" sent to root, generated by root and generated by
Alice.
So i do not know, if i have to tell the system, the services or Exim to
encrypt the messages.
Kindly waiting for your help and a hint in the wright direction, elrippo.