Diffie-hellman scheme

Question

Question 1:

a) Using Vigenere cipher and given the key abc, find out the ciphertext for the message:

Simplicity

Only the 26 lower-case alphabetical characters are used in the messages.

b) Compare and contrast Data Encryption Standard (DES) with AES (Advanced Encryption Standard) with respect to:

i) Their classification.
ii) Their encryption or decryption structure and algorithm.
iii) Their cryptographic strength.
iv) Types of attacks.
v) Hardware or software implementation.

c) Consider a Diffie-Hellman scheme with a common prime q = 11 and a primitive root α = 2.

i) If user A has public key Y_A = 9, what is A's private key X_A?
ii) If user B has public key Y_B = 3, what is the shared secret key K, shared with A?
d) What are the characteristics of the ‘one-time pad’ cryptosystem as compared to the Vigenere Cipher?

Give one advantage and two problems with one-time pad cryptosystems.

e) S/MIME (Secure/Multipurpose Internet Mail Extensions) is a standard for public key encryption and signing of e-mail encapsulated in MIME.  What are the cryptographic security services for electronic messaging applications given by S/MIME?