Cryptography & Network Security

2. (20 points) RSA Encryption. Bob wants to generate an RSA key-pair so that he can receive encrypted messages addressed to him. Suppose the message to be encrypted is M = 7 and the primes chosen are p = 11 and q = 13. Assume that e = 11 was selected to be his public exponent. (a) (5 points) Compute N, (N) and d, Bob's private key. (b) (5 points) Compute the ciphertext C when encrypting M using Bob's public key. (c) (5 points) Explain how Bob can decrypt the ciphertext obtained in Part (b) using his private key and compute the output of the decryption. (d) (5 points) Explain how an attacker, Eve, given only C can produce a new valid cipher- text C" that decrypts into something different than M