A NAT router is a device that allow many computers to share the same IP address. You can learn more about NAT itself from Internetworking with TCP/IP, Vol 1 (5th Edition). One drawback of using NAT is that to communicate with someone outside the private network, you must initiate the communication from the private network. This is all fine for contacting a web server but this is making peer to peer applications such as file sharing or gaming harder. There are some techniques to perform NAT traversal but what makes the matter worse is that NAT routers have a different NAT behavior from a model to the other and as if it was not bad enough, these behaviors are totally undocumented. Things are about to change as the RFC 4787 describes a set of behaviors that a router should have to be gaming friendly. So my advice as a person who has worked at Quazal, a big well known multiplayer online middleware company, if you want the best NAT router for online gaming for your video game console (Xbox, Xbox360, Nintendo Wii, Playstation 2, Playstation 3 or PSP), you should look for a router that is RFC 4787 compliant. They might be hard to find now as the RFC has been released just few months ago but if I personnally was looking to purchase a new router, that is what I would be looking for.
The basic principle to perform NAT traversal is that you need a server on the public network that will be used as a traversal probe relay. Lets say that client A and client B that are located behind 2 distinct NAT routers. They first have to contact the server. The server must keep the address from which it receive data from the clients. These addresses are the public address of the clients behind the NAT router as seen from the server. When client A wants to establish a connection with client B, it will first request the client B public address from the server and start sending probes to B public address. At the same time, client A will send a request to B by using the server as a relay to start sending probes to itself. What will happen is since both clients try to establish a connection with each other at the same time, there should be a midair collision where a hole has been created for the other on each of their respective router. This technique is called hole punching and there is an RFC describing a protocol that implement this principle. The protocol name is STUN (Simple Traversal of UDP for NAT).
NAT traversal for TCP is much harder because TCP handshaking for establishing a connection is asymmetric. To workaround that problem, you have to trick the TCP protocol and the router that might monitor the TCP handshake. There is not yet an official protocol but some proposals exist. One of them is STUNT (STUN for TCP) but the name is funny because it has also a second meaning. The way STUNT works is that both side will initiate a connection by sending a SYN packet with a short TTL (Time To Live). The TTL value must be carefully choosen so the packet goes out of the private network but does not reach the destination. Then the stack itself or a packet sniffer must read the sequence number contained in the SYN message and send the read value to the STUNT server. The server will then impersonate the other endpoint and spoof the SYN/ACK reply. Then the last step of the connection which is to send the final ACK can be sent as usual and if everything has worked fine, the TCP connection will be established normally. I will stop the NAT traversal explanation here as there are a lot of good resources on the net. Here are the most interesting:
Update (12/05/2010): I have written a review of Linksys and a Netgear gaming router if it can help you to choose the right router for your needs.
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