(a) An opponent is using RSA with the public key {e=53, n=77}. You intercept the ciphertext C=10. (All values on this problem, including the ciphertext and the cleartext, are numeric.)

(i) Deduce p and q.
(ii) Evaluate her private key.
(iii) What is the cleartext?

(b) Describe the terms ‘prime number' and ‘prime factorisation'. Illustrate the importance of prime numbers in cryptography.

(c) Consider cryptographic hash functions. Name four essential properties for a cryptographic hash function, explaining for each why it is essential.

(d) Explain the following techniques used by firewalls to control access:

(i) Packet Filtering
(ii) Proxy Server
(iii) Stateful Inspection