Question $3(10$ points$)$

$$ Public Key Encryption Algorithm $-$ RSA: Consider RSA with $p=3$ and $q=11,$ and the message $m=4.(2$ points$/$ each questions below$)($should be explained clearly and you should show all possible detailed steps.$)2$ points per question.

$($a$)$ What are $n$ and $z?$

$($b$)$ Let e be $9.$ Why is this an acceptable choice for e$?$

$($c$)$ Find $d$ such that ed mod $z=1($that is$,$ ed $-1$ is exactly divisible by $z,$ hence, there is no remainder.$)$

$($d$)$ What is an encrypted message? Show all work.

$($e$)$ Show how to recover the entrvnted message. Show all work.

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