This process is known as encryption. $($This particular encryption scheme is known as the one$-$time pad.$)$ We then send this output to our intended recipient. What we want to know is whether our intended recipient will be able to read it $($using their key$)$ and whether someone else would be able to read it $($without the key$).$

Prove that if the intended recipient takes the output and adds the key to it again $($using modular arithmetic$),$ then they will get the original message again. $($Hint: what happens if