I have a private cross-connection with a service provider
This private connection is connected from my firewall to their router and the L3 IP range /30 for this segment is private
However, i just realized that when they provided us their application IP to connected to over this connection is a public IP
The source IP i am using is actually still a private IP but yet the destination i am connecting to is a public IP and this is done over a private cross-connect with a private /30 transit network
Can a public IP transverse a private network ? I mean this cross-connection is not facing the internet - how does it work ?
If this is Pure Private, there is no exit point to internet here.
So the path only to use your network to to got Internet to reach the destination. Make small diagram for us to undertand this connection of your networks.
As i understand you have HQ with Interent conenction, your branch generally conntect using Private Line to HQ, so branch have always default route to HQ, on HQ you have infrastructure to NAT all RFC 1918 address when you sending to internet, this most standard setup used all over.
we would like to know your use case.
in short, if it is a private network, you can use ANY IP address (a public one in your case) you want. It is obviously a waste of address space, but it will work just fine.
An IP address is an IP address. Public and Private are artificial labels. What makes an address "private" is a loose agreement that no one will route it over the public internet. However, within one's own network, one may do whatever they wish. While it's a bad practice to mix private and public traffic, there's nothing logically wrong with it. "192.168.1.1" can talk to anything that knows how to get back to it; the internet at large won't have a route, but inside an ISP's network, anything goes. unionwells france
(This may work because the ISP is internally translating your "private" network. I've seen this done a few times, and it can be very confusing if you don't know about all the address translations. If it's not your mess to manage, take it at face value that it works.)