Part I. $(60\%)$ Encryption$/$Decryption using RSA:

Use p $=17,$ q $=11,$

n $=$ p$*$q $=17\backslash$times $11=187,$ and

$\backslash$phi $($n$)=($p $-1)($q $-1)=16\backslash$times $10=160$

$($a$)$ Let e $=13$ be the public key $($or $\{13,187\}$ be the public key$),$ and compute its associated private key for RSA.

$($b$)$ Use RSA with this pair of public$/$private keys to encrypt the plaintext message $77.$ What is its ciphertext message?

$($c$)$ Then encrypt the plaintext message $185.$ What is its ciphertext message?

$($d$)$ Given the ciphertext message $2.$ What is its plaintext message after decryption?

$($e$)$ Given the ciphertext message $150.$ What is its plaintext message after decryption?