April 2000
SC223 : COMPUTER SECURITY

QUESTION 2

Total Marks: 15 Marks

• Question 1
• Question 3
• Question 4
• Question 5
• Cover Page

SUGGESTED SOLUTIONS
Solutions and allocated marks are indicated in green.
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(a)Explain the differences with respect to key management between public-key and private-key cryptography.[4 marks ]
Public- vs private-key cryptography:

• Private-key cryptography uses a single key (1 mark), which must be kept secret (1 mark). Public-key cryptography uses two keys (1 mark), one key must be kept secret, but the other should be made public (1 mark).

[4 marks]

(b)Name and describe the problem with private-key cryptography that is solved by public-key cryptography.[2 marks ]
One problem of private-key cryptography is the key exchange or key distribution problem (1 mark for suitable name). In order to communicate over an insecure channel, parties must first communicate over a secure channel in order to agree on a private key (1 mark). [2 marks]

(c)Identify the components of a public-key cryptosystem,and explain the properties they must have.[6 marks ]
In a public-key cryptosystem, each party A has a public key P_A and a secret S_A (2 marks). An encryption algorithm E takes a key K and a message M, and generates a new message M’ = E(K, M) (1mark). The two keys should be inverses, in the sense that E(P_A, E(S_A, M)) = M and E(S_A, E(P_A, M)) = M for every party A and message M (2 marks). Moreover, it should be infeasible to compute the secret key S_A from the public key P_A (1 mark). (Actual notation doesn’t matter, as long as it is consistent; subtract 2 marks for inconsistency.) [6 marks]

(d)One can use public-key encryption also for signing messages. However,doing so increases the possibility of insecurities.One well-known such insecurity arises if the recipient of a message encrypts and signs it and sends it back as conformation of receipt.
(i)Explain how time-stamps foil this attack.[2 marks ]
(ii)Describe another way of foiling the attack.[1 mark ]
The ‘resent receipt’ attack:

(i) The attack involves the attacker resending a message (1 mark). If the message is time-stamped, the recipient can tell that it has been resent (1 mark).

[2 marks]

(ii) Using different algorithms (or keys) for encryption and for signatures foils the attack; so does avoiding sending back a receipt of apparent gibberish. (1 mark for either answer.) [1 mark]