$1.$ Imagine you are tasked with providing information security for a communication setup in which two parties, A and B $,$ wish to communicate by sending a single binary message from A to B $.$ However, an eavesdropper, E$,$ is capable of listening in on the transmission. Party A decides to XOR the message with a sequence X to hide its contents from E$.$

$($a$)$ Define the problem of designing X$.$

$($b$)$ Are there any assumptions needed?

$($c$)$ Propose a solution to this communication problem.

$($d$)$ Are there any limitations to your solution?