Exercise $1$:

In an RSA cryptosystem the two prime factors $p$ and $q$ of the RSA modulus $n,$ were chosen as $p=17$ and $q=11.$ Answer the following, showing your detailed computations.

The RSA modulus, $n.$

Euler's phi function, $(n).$

Assume that the encryption exponent was chosen as $e=7,$ compute the decryption exponent, $d.$

Using the above information encrypt the message $m=88.$

Using the decryption key, decrypt the obtained ciphertext in $4)$ above.