"we've got an arbitrary security restriction that says "UDP port 111 (rpcbind)" shouldn't be open!"
As an observarion to this statement and as a response to UDP port scanning in general you may be interested in reading The art of port scanning:
"UDP ICMP port unreachable scanning : This scanning method varies from the above in that we are using the UDP protocol instead of TCP. While this protocol is simpler, scanning it is actually significantly more difficult. This is because open ports don't have to send an acknowledgement in response to our probe, and closed ports aren't even required to send an error packet. Fortunately, most hosts do send an ICMP_PORT_UNREACH error when you send a packet to a closed UDP port. Thus you can find out if a port is NOT open, and by exclusion determine which ports which are. Neither UDP packets, nor the ICMP errors are guaranteed to arrive, so UDP scanners of this sort must also implement retransmission of packets that appear to be lost (or you will get a bunch of false positives). Also, this scanning technique is slow because of compensation for machines that took RFC 1812 section 18.104.22.168 to heart and limit ICMP error message rate. For example, the Linux kernel (in net/ipv4/icmp.h) limits destination unreachable message generation to 80 per 4 seconds, with a 1/4 second penalty if that is exceeded. At some point I will add a better algorithm to nmap for detecting this. Also, you will need to be root for access to the raw ICMP socket necessary for reading the port unreachable. The -u (UDP) option of nmap implements this scanning method for root users.
Some people think UDP scanning is lame and pointless. I usually remind them of the recent Solaris rcpbind hole. Rpcbind can be found hiding on an undocumented UDP port somewhere above 32770. So it doesn't matter that 111 is blocked by the firewall. But can you find which of the more than 30,000 high ports it is listening on? With a UDP scanner you can!"
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