Question $2$ Classical and Block Ciphers $(50$ marks$)$

$($a$)($i$)$ Use the Caesar cipher with the key T to encrypt the plaintext COMMITTEE. You

may assume that A $=1,$ B $=2,...$ Z $=26$ and a space is represented by $0,$ and

that arithmetic is carried out mod $27.$

$3$ marks

$($ii$)$ Use the Vigen$$re cipher with the keyword WASP to encrypt the plaintext

COMMITTEE. You may assume that A $=1,$ B $=2,...$ Z $=26$ and a space is

represented by $0,$ and that arithmetic is carried out mod $27.$

$3$ marks

$($iii$)$ Use the examples in parts $($i$)$ and $($ii$)$ to illustrate the effect that the Vigen$$re cipher

has in smoothing out the letter frequencies in the ciphertext.

$7$ marks

$($iv$)$ Explain briefly why smoothing out the letter frequencies is a useful feature of a

symmetric key cryptosystem.

$5$ marks

$($iv$)$ Describe the one time pad and explain why it offers perfect security. What are the

difficulties which deter people from using such a system?

$6$ marks

$($b$)$ A symmetric key block cipher with key k is used. The encryptions of all possible $4-$bit

plaintext blocks are given in the table below.

Plaintext Ciphertext Plaintext Ciphertext Plaintext Ciphertext

$000010000110010110111100$

$000111010111111111001110$

$001000011000011011010000$

$001101111001001011100011$

$010001001010100111111011$

$01011010$

Table $1$: Plaintext blocks encrypted with the symmetric encryption algorithm

Suppose you receive the ciphertext message, C $=101101010111.$ To answer the

following questions, you may assume that all initial values are $0.$

$($i$)$ Use the ECB mode of operation to decrypt the message.

$4$ marks

$($ii$)$ Use the CBC mode of operation to decrypt the message.

$7$ marks

$($iii$)$ Use the CTR mode of operation to decrypt the message.

$7$ marks

$($iv$)$ Explain why you might choose to use CBC instead of ECB.

$4$ marks

$($v$)$ Give one advantage of using CTR instead of CBC$.$