I don't understand how the ISP can assign Public IPs to routers that newly join their network, without having DHCP or ARP messages amplified millionfold.
As far as I know, for a L3 router to join a network at all, the joining entity has to talk with the DHCP server to get an IP address. DHCP discover messages are broadcast with MAC FF:FF:FF:FF:FF:FF, and to the whole subnet. And so, if the router is newly connected to a WAN with thousands, if not ~100000s of other routers, I would imagine the result to be a DHCP discover message that reverberates and amplifies until its TTL expires – which is certain to either a) fail to reach target or b) cause millions, not if billions, of other messages.
And, facing the same direction, I can apply the same argument to ARPs. ARP messages are broadcast as well around the network, just like the DHCP discover, and so the same set of problems would arise.
I can probably apply the same argument to messages used by the Network layer to coordinate its routers with distance-vector algorithm, unless the routers are somehow organized in a tree or graph-like manner, but I digress.
Where have I gone wrong?
Best Answer
You make a lot of assumptions that simply aren't true.
Topologies vary, but an ISP's network is not one flat broadcast domain, so broadcasts aren't amplified a million-fold. Routers block broadcasts, so they are limited to one subnet.
ISPs can filter broadcasts further, and do many other "tricks" to limit DHCP and ARP messages to a small set of devices.
One more thing: distance vector routing algorithms (like RIP) are essentially obsolete. ISPs generally use OSPF or IS-IS internally, and BGP to connect with their customers and peers.