I have a router behind the ISP router that provides internet over DHCP to the router.
I wanted to take up the public address so I wouldn’t have to ask them for port forwarding, so I asked them to provide me with IP/network and gateway so I can enter that in IP/Address and Routes.
They replied asking me if I need public IP and to provide private IP for NAT-ing from public to private IP.
I am not sure what exactly that means, and would appreciate some pointers.
My assumption is they want to configure what they call these day “DMZ”, i.e. forward all ports to the private IP of your router (In my view, term DMZ in this config is not the correct terminology)
That is what it seems to me too. What should I tell them (not sure about terminology)? I just want to take over the public IP where they are the gateway and provide access to the internet.
You want them to put their CPE router in bridge mode. No idea whether your ISP supports that; not all do. Another possibility is replacing their router with your own and terminating the link directly yourself, but even fewer ISPs will let you do that (mine happens to).
I’m not sure bridge mode is a possibility if you also have telephony. You can still replace their router with your own if they will let you and if they will tell you how to configure it. My provider has SIP telephony, IP TV and basic Internet service (or combination thereof) and will tell you what and how you need to configure your stuff to make it work, but they won’t support you if you can’t figure it out by yourself; they just give you the basic info you need.
You can ask them if they will put the router in bridge mode, but don’t be surprised if they say ‘Sorry sir, we can’t do that, as you also have telehony from us’ (or just ‘Sorry, no can do’). If so, ‘DMZ mode’, where they simply forward all incoming connections to you, is probably as good as it gets. And that’s likely what they wanted to do in the first place, as they asked you for a private IP to NAT for.