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TCP/IP Guide by Charles M. Kozierok

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IP NAT Overlapping/Twice NAT Operation

All three of the versions of NAT discussed so far—traditional, bidirectional, and Port-Based—are normally used to connect a network using private, nonroutable addresses to the public Internet, which uses unique, registered, routable addresses. With these kinds of NAT, there will normally be no overlap between the address spaces of the inside and outside network, since the former are private and the latter are public. This enables the NAT router to be able to immediately distinguish inside addresses from outside addresses just by looking at them.

In the examples you've seen so far, the inside addresses were all from the RFC 1918 block 10.0.0.0. These can't be public Internet addresses, so the NAT router knew ...

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