27 Dec For the first post, select a problem fro

MAT2051 Discrete Mathematics

Unit 6 Discussion

DQ1 Cryptography and Security

Cryptography is an exciting IT field that focuses on secure communications, typically on a network. Many encryption methods use number theory to encode and decode messages. This number theory typically draws upon ideas such as prime factorization, greatest common divisors (GCD), modulus, and so on.

For this discussion, read Chapter 5, section 5.4, which starts on page 250 of your text, which discusses number theory and applications to cryptography. Post an explanation of how the RSA public-key cryptosystem works that includes answers to the following questions:

What is a key?

What are public and private keys, and how are they used in the RSA public-key cryptosystem?

How are messages encoded and decoded using mod and GCD?

If you are using p = 17, q = 23, and n = 31, what would the encryption of 101 be, using public key z = pq?

Where is security used, and why is it important to everyone?

Review the Discussion Participation Scoring Guide prior to posting. Make sure you include a minimum of three posts and that your first, or main, post responds to all parts of the question posed.

Response Guidelines

Read your peers’ posts and respond to two. Did you reach the same encryption as your peer? Explain why or why not. Show your work.

DQ2 Practice Problem Set Review

This discussion allows you to work with your peers to complete and understand the assigned problem set for this unit. Remember, two initial posts and two response posts are required. Further posts are optional and recommended:

For the first post, select a problem from this unit’s problem set, write it out fully, solve it fully, and post it.

The second post can be a problem you cannot solve or another fully solved problem from the problem set. If there is a problem in the problem set that you are confused about, write it out fully and show any work that you have started. Note that you are stuck and ask for help. If you are able to solve every problem in the set without difficulty, post at least one other fully solved problem from the set as your second post.

The third and fourth posts are responses. Response guidelines are provided below and in every discussion.

Take advantage of this discussion area to work together as a class on the problem set. Post as many problems as you can and review as many of your peers’ posts as you can. Ask questions. Offer answers. If you are stuck on a problem, post your question. Working as a team will help each person gain a better understanding of the problem set and the concepts covered in this unit. Although the problem sets are not graded they will help you prepare for the quizzes in this course.

MAT2051 Discrete Mathematics

Unit 7 Discussion

DQ1 Computer Networks, Distributed Systems, and Mobile Agents

Computer networks typically consist of nodes and edges—they are graphs. The nodes can typically be computers, routers, servers, and so on. The edges indicate a communication path between nodes. Assume you are a network administrator for a distributed system and that you wish to perform maintenance of all the servers in your system. You have decided to do this by using a mobile agent. To get started, look up and answer the questions in Part 1. After that, complete Part 2:

Part 1

What is a distributed system?

What is a mobile agent?

Since this agent is autonomous and moves from computer to computer, it would be smart to equip it with shortest path algorithms, so that it can go from server to server, reaching all the servers only once, in the shortest amount of time. This is the traveling sales person (TSP) problem. Note that computer networks can be modeled using graphs and that shortest paths solutions, Hamilton cycles, TSP, and so on can be found using graph-based algorithms.

Part 2

How would you model a computer network using a graph? What are potential nodes, edges, and weights?

Which of these traversal algorithms should the agent be equipped with? Which will help the agent traverse the network in an efficient manner? Explain why.

What is the TSP problem, and how does it relate to this question?

Review the Discussion Participation Scoring Guide prior to posting.

Response Guidelines

Read your peers’ posts and respond to two. Compare your response to your peer’s response. Did you come up with the same results? Explain why or why not.

DQ2 Practice Problem Set Review

This discussion allows you to work with your peers to complete and understand the assigned problem set for this unit. Remember, two initial posts and two response posts are required. Further posts are optional and recommended:

For the first post, select a problem from this unit’s problem set, write it out fully, solve it fully, and post it.

The second post can be a problem you cannot solve or another fully solved problem from the problem set. If there is a problem in the problem set that you are confused about, write it out fully and show any work that you have started. Note that you are stuck and ask for help. If you are able to solve every problem in the set without difficulty, post at least one other fully solved problem from the set as your second post.

The third and fourth posts are responses. Response guidelines are provided below and in every discussion.

Take advantage of this discussion area to work together as a class on the problem set. Post as many problems as you can and review as many of your peers’ posts as you can. Ask questions. Offer answers. If you are stuck on a problem, post your question. Working as a team will help each person gain a better understanding of the problem set and the concepts covered in this unit. Although the problem sets are not graded they will help you prepare for the quizzes in this course.