QUESTION $3$

a$)$ In a public key cryptosystem, you do not need to keep the encryption key secret. Why is it essential to keep the encryption key secret in a symmetric key cryptosystem?

b$)$ In a symmetric key cryptosystem, what do the terms blocksize and keysize mean? Why is it important for a symmetric cryptosystem to have a large blocksize and a large keysize?

c$)$ What is the main difference in the way in which data is encrypted by a stream cipher and a block cipher?

d$)$ Why are stream ciphers used in implementations where a lot of interference might be expected such as mobile telephone communications?

e$)$ A block cipher should have the properties of diffusion, confusion and completeness. Explain each of these properties and why they are essential for a secure block cipher.

f$)$ Triple DES and Rijndael are two widely used symmetric key ciphers. State one advantage and one disadvantage of Rijndael when compared to Triple DES.

QUESTION $4$

a$)$

$($i$)$ Describe the key generation protocol for the RSA public key cryptosystem.

$($ii$)$ Suppose that an algorithm is found that can efficiently factorise a large number. Explain how a cryptanalyst could use this algorithm to break the RSA cryptosystem.

b$)$ Below is a simple method for blocking and encoding upper$-$case letters for encryption.

Group letters into blocks of two starting at the leftmost letter. Add a space character at the rightmost side if necessary to make an even number of characters.

Encode letters using $A=1,B=2,$dots,$Z-26,$ space $=0.$

Convert each block of two characters into a single decimal number by multiplying the value of the first character by $27$ and then adding the value of the second character.

Thus, the word STARS is partially encoded as follows:

$\backslash$table$[[$characters$,S,T,A,R,$S space$],[$character values,$19,20,18,],[$block value,$\backslash$table$[[19(27)+20$