Computer Science Assessment - Network Security

201390 ITC593

Assessment Item 2

Tasks

Task 1 (25 marks)

a) Consider the table in Figure 2.5 on page 66 of the textbook showing the relative frequencies of letters in English. Arrange the frequencies from largest to smallest, and make a cumulative plot, using Excel for example. Which smallest group of letters accounts for at least 50% of all letters used in English?

b) An affine cipher scheme can be mathematically expressed in the following form

Here and are numbers selected in the range , and represents a letter converted to a number using the rule .

i) What are the and values for the Caesar cipher?

ii) Encrypt the plaintext “MOUNTPANORAMA” using .

iii) Why is not a good choice of affine cipher parameters when there are 26 letters in the alphabet?

c) Do exercise 2.3 on page 85 of the textbook.

Task 2: 20 marks

a) The keyspace for a cipher is the set all of possible keys that can be used for the cipher. A DES key consists of 56 (independent) bits.

i) Express the size of the DES keyspace to the nearest power of 10, and find three examples of physical quantities, or other known values, that are approximately the same size.

ii) Consider the collection of passwords defined by combinations of digits and letters (both upper and lower case). What password length would be required so that the number of possible passwords is at least the size of the DES keyspace?

b) Encryption is only useful if there is a matching reversible operation called decryption. In a Feistel cipher, the F-function or round function need not be reversible.

i) Show that F-function of DES is not reversible

ii) Explain how a Feistel cipher whose main component is not reversible can actually support decryption.

Task 3: 20 marks

a) Let denote the DES encryption of the plaintext P by the key K.

i) If we set K to be the key consisting of all zeroes, explain why encrypting twice with this key for DES has the same effect as encrypting then decrypting. Equivalently, account for the following property when using the all-zero key

ii) Find another key that also has this property, and explain the structure of the DES key schedule that permit such keys to exist.

b) Let denote the complement of a sequence of bits, so that for example Then considering the round structure of DES, show that

In other words, complementing the key, plaintext and ciphertext produces the same ciphertext as when none of these values is complemented. Hint: Use the following property of the XOR function .

Task 4: Understanding RSA (15 marks)

The general method for constructing the parameters of the RSA cryptosystem can be described as follows

· Select two primes and

· Let and determine

· Randomly choose in the range such that

· Determine as the solution to

· Publish as the public key

a) Show that a valid public key pair can still be constructed if we use only one prime , such that and .

b) If we use this “one-prime” RSA construction and publish the public key why is it easy to recover the secret key

c) Let denote the encryption of the message using the pair Show that the RSA encryption function has the following property for any two messages and

That is, the encryption of a product is equal to the product of the encryptions.

Marking Scale

Task 1 (25 marks)

a) Clear, well-labeled graph and correct answer to letter set (5 marks)

b) 15 marks in total 

i) Correct answer (1 mark) 

ii) Correct answer, showing the transformed alphabet (5 marks)

iii) Convincing argument supported by worked example (4 marks)

c) Presentation of the argument or proof, using equations, to recover the affine cipher parameters (5 marks)

Task 2 (20 marks)

a) 10 marks in total 

i) Correct power of 10, and 3 examples with evidence (5 marks)

ii) Correct password length with working shown (5 marks)

b) 10 marks in total 

i) Example showing that part of all of the DES round function cannot be reversible (5 marks)

ii) Correct written description supported by diagram (5 marks)

Task 3 (20 marks)

a) 10 marks in total 

i) Correct argument involving interaction of key schedule, encryption and decryption of DES (5 marks)

ii) Correct identification of the additional key, and convincing explanation of the DES key schedule property that produces equivalent keys for encryption and decryption (5 marks)

b) Correct argument for explaining the reason for the complementation in DES, using diagrams involving the round function (10 marks)

Task 4 (15 marks)

a) Show that “one-prime” construction produces a valid public key (5 Marks)

b) Show the steps to recover (5 Marks)

c) Mathematical argument to show the property (5 Marks)