INT20CN Computer Networks

Tutorial #20

1. What are the advantages and disadvantges of a public key cryptosystem compared to a single key system? Draw a table giving at least one advantage and one disadvantage of each system, mentioning such problems as key management and encryption/decryption speed.

2. In the RSA example given in the lecture, what aspect of the system makes it difficult to discover Ks (the decryption, or private key) given that you know Kp, the public encryption key?

3. One of the major disadvantages of a public key cryptosystem based on RSA is its slow speed of encryption and decryption. Explain briefly why the RSA algorithm is slow compared to a single-key encryption system such as DES. How can public key and single key encryption be combined to give a secure, but fast, encryption system?

4. In the public-key authentication protocol given in the lecture notes, in message 3 (sent from A to B), RB is encrypted with Ks. Is this encryption necessary, or would it have been adequate to send it back in plaintext?

5. What is the difference between a digital signature and a message digest? What are the advantages and disadvantages of each?

6. In the lecture notes, it was claimed that no one can generate two messages that have the same message digest. How can the system designer ensure this?

7. The Unix system uses a scheme with some similarities to a message digest for storage of user passwords. In what ways are these similar? NB: if you don't use Unix, or use it infrequently, you may be excused from this question.

8. (Requires basic mathematical skill. This will probably not be on the exam!) Using the RSA cryptosystem with p = 7 and q = 11,
   1. Write down the values of n and X.
   2. Find a suitable value for E. What is the public key Kp corresponding to these values?
   3. Discover a legal value for D. What is the private key Ks corresponding to these values?

9. (Advanced - maths majors only. This will not be on the exam!) Again using an RSA cryptosystem, this time with p = 13, q = 31 and D = 7, find E.

10. (Advanced - maths majors only. This will not be on the exam!) Using the results of the previous question for p, q, D and E,
    1. Ascertain the largest message size (in bits) which can be encrypted using these values, and
    2. Demonstrate the encryption and decryption of a message.

11. (Very advanced - maths majors only. This will not be on the exam!) In the lecture, a demonstration was given of a RSA-like public key encryption system, albeit one using very small primes. The numerical results were given without justification. Attempt to verify the correctness of the calculations presented there.