[Exim] No unauth smtp from local accounts

Hi,

I want to set up Exim 4.30 to (number 2 is not working):

1. Just auth'ed connections have permission to relay (this is working)
2. Unauth'ed smtp is just received if not sending from local account.

Ie. What I want to do is to make sure that I can receive mail from external
smtp servers and that auth'ed accounts can relay mail wherever they want.
The problem with my current setup is that it's possible to send mail from
one local account to another local account from the internet without
auth'ing at all.

Anyone have the solution to this problem, maybe as described in number 2 or
in some other way?

Regards,
Stefan

---

Here's a snippet from my current exim4.conf

acl_check_rcpt:

# Accept if the source is local SMTP (i.e. not over TCP/IP).
accept hosts = :

# Accept everyone that authenticated
accept authenticated = *

# Deny if the local part contains @ or % or / or | or !.
  deny    local_parts   = ^.*[@%!/|]

# Block spoofed addresses
  deny    condition     = ${if eq
{$sender_address_domain}{$local_part@$domain}{yes}{no}}
          hosts         = !+relay_from_hosts

# Accept mail for us
  accept  domains       = +local_domains
          hosts         = !+relay_from_hosts

# Else: Go away
  deny    message       = relay not permitted