Show your work and intermediate steps. Question 1 [30 points]: Perform encryption and decryption using the RSA algorithm, for the following a) p= 3; q 11, e 7;M=5 b) p = 11; q=13, e = 11; M = 7 Question 2 [20 points]: Use modular exponentiation to answer the following questions: Note: you need to show your work and the intermediate exponents must be equal or less than 4 1. 1220 mod 71 = 2. 1315 mod 41= Question 3 [20 points): In a public-key system using RSA, you intercept the ciphertext C = 20 sent to a user whose public key is e = 13, n = 77. What is the plaintext M? Note that M has been encrypted using the public key. Question 4 [30 points]: Alice and Bob use the Diffie-Hellman key exchange technique with a common prime q-23 and a primitive root a=5. (a) If Bob has a public key Yo=10, what is Bob's private key Xa? (b) If Alice has a public key YA-8, what is the shared secret key K with Bob?