Computer Networks

Tutorial #19

1. What are the advantages of a public key cryptosystem compared to a single key system? Why is the problem of key management almost as difficult in public key systems as it is in single key systems?

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. 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?

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

5. 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?

6. 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.

7. (Advanced - maths majors only. This will not be on the exam!) Using the RSA cryptosystem with p = 7 and q = 11, list 3 legal values for D.

8. (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.

9. (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.

10. (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. Verify the correctness of the calculations presented there.