COMP 6461 - Theory Assignments

Comp6461 – Fall 2014 Theory Assignment 3 - Page 1

COMP 6461 - Fall 2014

Theory Assignment 3

1) What is the main difference between Pure Aloha and Slotted Aloha? Are there any circumstances where Pure Aloha would perform better than Slotted Aloha? If so, give

such circumstances/conditions. If no, explain why Pure Aloha could never perform better

that Slotted Aloha.

2) Given a network with 9 routers as shown in the figure below. Assume the utilization of center-based spanning tree construction, where router D is assigned as the center (or

root) router. Assume routers join the tree in the following order: C, A, H, B, F, G, E, and

I. Show the final constructed spanning tree for that given network.

3) Consider two substitution ciphers. One adds a value of i to the ASCII code of the plaintext character. The other adds a value of j to the plaintext character. All additions are

modulo 256. Now consider a double-encryption method that adds i to each plaintext

character and then adds j to the resulting ciphertext character to get another ciphertext

character. Again, all calculations are modulo 256 How much more secure is this double

encryption when compared with either single-encryption method? Explain your answer.

4) Consider the bit string 001011010101000011111101001101 and the key 10110. Use the key to encrypt and then decrypt the string using bit level ciphering.

5) Suppose you were trying to crack an encryption method that used a 64-bit key. Assuming a brute force attack, how many keys per second must you try to crack the code in 30

days?

A

C

D

G

B

E

F

H

I

Comp6461 – Fall 2014 Theory Assignment 3 - Page 2

6) Three broad classes to multiple access techniques exist, which are: channel partitioning, random access and taking turns. In general, it is assumed that any network would use one

of these techniques or the other. However, cable Internet access networks utilize all three

techniques. Describe how this is done by such networks, and explain how the utilization

of any of these techniques does not conflict with the utilization of the other two.

7) In general, fully-connected topology is exhaustive and very unlikely to be used for the construction of a network.

a. Are there any clear and significant advantages of such topology? Explain clearly. b. Explain why it is unlikely that such topology be used for network construction.

You should clearly indicate the major disadvantages of such topology.

c. While this topology seems to make little sense for the construction of networks, in the general terms, it is actually used as part of Data Centers to connect Tier-1 and

Tier-2 switches. Explain clearly the major advantages of such utilization in data

centers. You should provide some example that shows, through some numerical

values, the obvious advantages of such utilization.

8) Assume the utilization of Hamming Codes for single-bit error correction.

a. What is the total number of bits that need to be transmitted if the original data

string has 11 bits? Which positions will be covered by the different parity bits?

b. What is the total number of bits that need to be transmitted if the original data

string has 19 bits? Which positions will be covered by the different parity bits?

9) Token Ring LANs have the clear advantage of avoiding collisions, which is surely not

the case for networks, i.e. Ethernet, that use buses as the main segment to connect the

different devices. In spite of that, Ethernet LANs are capable today of providing a

superior performance in comparison to Token Ring LANs. Explain how the Ethernet was

able to achieve that regardless of the collision issues. In particular, your answer should

consider: 1) the disadvantages of Token Rings, and 2) Switched Ethernet.