For each problem, you must show your work to get credit.

$1.$ Perform encryption using the RSA algorithm for the following

a$.$ p $=3,$ q $=11,$ e $=7,$ M $=5,$ C $=?$

b$.$ p $=5,$ q $=11,$ e $=3,$ M $=9,$ C $=?$

c$.$ p $=7,$ q $=11,$ e $=17,$ M $=8,$ C $=?$

d$.$ p $=11,$ q $=13,$ e $=11,$ M $=7,$ C $=?$

e$.$ p $=17,$ q $=31,$ e $=7,$ M $=2,$ C $=?$

$2.$ Perform encryption and decryption using the RSA algorithm for the following

a$.$ P $=61,$ q $=53,$ M $=35$

$3.$ In a public$-$key system using RSA, you intercept the ciphertext C $=10$ sent to a user whose public key is e $=5,$ n $=35.$ What is the plaintext M

$4.$ In an RSA system, the public key of a given user is e $=31,$ n $=3599.$ Write a program using Java, C#$,$ or Python to calculate the private key of this user. Also, copy and paste your source code below.

$5.$ Consider a Diffe$-$Hellman scheme with a common prime q $=11$ and a primitive root $\backslash$alpha $=2.$

a$.$ If user A has public key YA $=9,$ what is A$\text{'}$s private key XA$?$

b$.$ if user B has public key YB $=3,$ what is the shared secret key K$?$