If two primes $p=17,q=11$ are selected as well as number $e=7($as in Unit $5B$ slide $11),$ verify that $d=23($using the algorithm in Unit $5$B slide $9)$ and answer the following questions:

$($a$).$ What is the public key?

$($b$).$ what is the private key?

$($c$).$ Encrypt a message which is represented as $88$

$($d$).$ Decrypt the ciphertext you get from $($c$)$ to verify that the decrypted message is indeed $88.$

$($e$).$ Encrypt a message $78$

$($f$).$ Decrypt the ciphertext you get from $($e$)$ to verify that the decrypted message is indeed $78.$