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Let's say that we have a private network, with private addresses and a NAT enabled router at the end. If the router is misconfigured and routes traffic to the global internet, keeping as source address the private one, at which step of the path will a packet be filtered if it is sent by a local PC to a server that has a global IP? Could that packet reach a server? This question is purely theoretical obviously.

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IP has no concept of private or public addresses. For IPv4, we have RFC 1918 that set aside three address ranges for Private addressing, but all that really means is that the ISPs have agreed to not route packets with those addresses on the public Internet.

IANA maintains the IANA IPv4 Special-Purpose Address Registry, which has a table of the special address ranges, including Private address ranges. The table explains if the special address range is recognized by IPv4, itself:

Reserved-by-Protocol - A boolean value indicating whether the special-purpose address block is reserved by IP, itself. This value is "TRUE" if the RFC that created the special-purpose address block requires all compliant IP implementations to behave in a special way when processing packets either to or from addresses contained by the address block.

Address ranges that are True for Reserved-by-Protocol must be recognized and treated specially by an IPv4 implementation, but those that are False need special handling for special use by an end host, otherwise they are treated as normal IPv4 addresses, and IPv4 does not know about them.

Notice in the table that all three Private address ranges are False for Reserved-by Protocol.

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There's no precise answer. Most ISPs filter out private source addresses, but not all. If they don't, the packet could (in theory) reach the destination. However, the return packet would be stopped at the first router that has filtering or the first router with no default route.

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Firstly your question is not precise to answer ..

Basically when pc wants to communicate server hosted in internet it will check for routing or route table to reach the destination . To forward packet from souce to destination fallowing tables are verified

  1. ARP table
  2. mac -address table
  3. routing table
  4. NAT table

For example

When traffic is initiated from source pc witth private adress . It should reach edge router . Edge router should connected with ISP and ISP provided public ips should be configured as interface ip for egress interface and default route as to configure in router pointing ISP gateway and NAT policy should be configured in router ..

Packet flow

Traffic is initiated from pc with souce as private ip address allocated to pc . packet is forwarded to router . Router will verify destination address of packet and check for route in routing table and forwards packets to ISP gateway before forwarding it will do NAT translation from private address to public ip beacuse private ip address are not routeble in internet

Traffic is filtered on basic of access-list, route entries configured on edge routers At some point in traffic flow from source to destination there are specific routes configure at ISP level at this point packet will get dropped this might be happen for forward direction of packet or for reverse traffic of same session

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