Mathematics of Cryptography

Winter 2010 - Math 4161 3.0


Tuesday  2:30-4pm  TEL 0007,     Thursday  2:30-4pm  TEL 0005

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Professor Mike Zabrocki
Office: TEL 2028
Office Hours: Tuesday 12-1pm or by appointment
e-mail : my e-mail
web page: http://garsia.math.yorku.ca/~zabrocki
course web page: http://garsia.math.yorku.ca/~zabrocki/math4161w10/
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Course Description :Cryptography deals with the study of making and breaking secret codes.

In this course we will be studying situations that are often framed as a game between three parties: a sender (e.g., an embassy), a receiver (the government office) and an opponent (a spy). We assume that the sender needs to get an urgent message to the receiver through communication channels which are vulnerable to the opponent. To do this communication, the sender and receiver agree in advance to use some sort of code which is unlocked by a keyword or phrase. The opponent will be able to intercept the message. Is he/she able to unlock the message without knowing the key?

In this course we will learn some probability theory, information theory and number theory to answer questions about how vulnerable the methods of sending secrets are. This has a great number of applications to internet credit card transactions, wireless communication and electronic voting. We will start by learning some classical codes (used up through WWI) and analyzing those. The last third of the course we will start to learn the methods that are used in modern cryptography.


Announcements:

(January 5, 2010) (RULE #1) I will NEVER EVER post solutions to practice questions or quizzes. Don't ask. Email questions like "what is the answer to number xxxx?" will mostly be ignored. I will answer questions about the practice by email on an individual basis but I need to know what you tried to solve the problem.

(January 9, 2010) I posted another set of practice problems that could be on the quiz. The quiz could include anything that we covered in class (yes, that includes ADFGVX). Also look in the texts for the historical ciphers. There are practice problems that are also similar to the quiz at the end of each section.

(February 14, 2010) Happy V-day. I sent you all a message containing a cryptogram from Dr. Evil. If you didn't get one then look in your Spam box and then if it isn't there send me an email and I will issue another one. The due date for this assignment is Thursday, March 4. It shouldn't take more than a few minutes.

(February 24, 2010) I resent the Dr. Evil message to about 9 of you who had a corrupted file. I found out what the problem was and hopefully fixed it. Sorry about that.

(March 9, 2010) I realize that I didn't make exactly clear what you can conclude from the entropy about the decision tree so I inserted a slide in the "dirty slides" that states precisely what the entropy tells you.

(April 2010) Course evaluations are online. I would really like your feedback for this class and I am going to make it worth 2% on the final. You must do the evaluation by April 6, 2010! Please visit the site at: http://courseevaluations.yorku.ca/

(May 2, 2010) I want to give you the chance to review your grades in case you should notice a descrepancy between what you have and what I have recorded.

Text : I will not be following a textbook for the course. The last time I had a textbook I followed class notes much closer than we followed the book. The text that I used last time was 'Cryptography: an introduction' by Nigel Smart.  If you feel like you would like to have a reference book in addition to the class notes that I will provide you with, then I suggest that you search this book out. I expect the notes will prove to be more useful and it is important that you come to class to ask questions and. FYI, the book does not cover the introductory material on classical ciphers very well, but I like it.

Issues of Academic Integrity : Your exams and quizzes will be open books and notes. I want you to have access to reference material when you are working. I expect you however to keep your eyes on your own paper. Students are expected to be familar with the Senate Policy on Academic Honesty and to follow it. The last time that I taught this class I had at least two people pass through hearings with the administration because of issues with academic dishonesty. This time I will not take chances and I intend to put as many mesures into effect to stop cheating as possible.

Calculators that use + - * / ^ and log are allowed on quizzes and tests. Calculators which have more advanced functions like factor, gcd, Jacobi, mod and discrete log are not commonplace and until those functions are available to everyone I expect you to stick with a basic calculator. No smart phones. Books and notes are allowed on the tests and quizzes as well but I try to add some creative way of making the problems unique so that they are not the same as changing a few numbers from a practice problem. It is not my job to watch over your shoulder to tell you the difference between right and wrong. I give you a lot of leeway (e.g. open book and notes, and calculators) in this class because I expect you to be honest and follow these rules and not copy off of your neighbor when we have tests and quizzes.

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