The IP packet header contains a $16-$bit ID field. The protocol standard states that the ID field should differ between different packets sent by a source to a given destination. A common method that hosts use to implement the ID field is to maintain a single counter that the host increments by one for every packet it sends, regardless of to which destination it sends it$.$ The host sets the ID field in each packet it sends to the current value of the counter. Since with this implementation the host uses a single counter for all of its connections, we say that the host implements a global ID field.

$($a$)$ Suppose a host P implements a global ID field. Suppose further that P responds to ICMP ping requests. You control some other host A$.$ How can you test if P sent a packet to anyone $($other than A$)$ within a certain one minute window? You are allowed to send your own packets to P $.$

$($b$)$ Your goal now is to test whether a victim host V is running a server that accepts connection to port X $($that is$,$ test if V is listening on port X$).$ You wish to hide the identity of your machine A$.$ Hence, A cannot directly send a packet to V $,$ unless that packet contains a spoofed source IP address. Explain how to use P to do this.

Hint: The trick here is to send TCP packets to V with the spoofed source IP address. Recall the following facts about TCP$.$

$$ A host that receives a SYN packet to an open port X sends back a SYN$/$ACK response to the source address.

$$ A host that receives a SYN packet to a closed port X sends back a RST packet to the source address.

$$ A host that receives a SYN$/$ACK packet that it is not expecting sends back a RST packet to the source address.

$$ A host that receives a RST packet sends back no response.

$($c$)$ How would you change P to avoid this problem? You are not allowed to modify the TCP$/$IP protocol or the services running on P$.$ You may only modify the implementation of TCP$/$IP on P$.$