[exim] DKIM signing for multiple domains

Hi everyone,

I have multiple domains hosted on the same server. They are virtual
domains. The server has just one IP address and one Exim instance.
I am wondering how to easily do DKIM signing for these domains. I decided
to use the same selector for all the domains to make life easy. Would the
following transport work? If not, what is the best way to do this for
multiple domains sharing the same IP address?

remote_smtp_DK:
driver = smtp
dkim_domain = ${sender_address_domain}
dkim_selector = csl
dkim_private_key =
"/etc/pki/tls/dk/${sender_address_domain}-dkim.priv.key"
dkim_canon = relaxed
dkim_strict = true

--
Best regards,
Odhiambo WASHINGTON,
Nairobi,KE
+254 7 3200 0004/+254 7 2274 3223
"Oh, the cruft."