Part B $[14$ pts$]$

The RSA cryptosystem

Wessam uses the RSA cryptosystem from the prime number theory to allow people to send encrypted messages. Wessam selects the parameters:

$p=17,q=41,e=61$

$[7$ Pts$]$ Support Wessam by calculating the private key. Calculate and state the private key. $($You must use the extended Euclidean algorithm and show all steps to deserve the credit$).$

$3$

$[7$ Pts$]$ Wessam received the ecrypted ciphertext $c=644.$ Support Wessam by decrypting the ciphertext $c$ and give the original message $m.($You must state all the used equations and use the fast exponent algorithms in your calculations. Show all steps to deserve the credit$).$ solve for both questions