Mathematics of Cryptography

Math 4161 3.0
Tuesday, Thursday 2:30-4pm    CB 115

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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:
course web page:
TA: Anouk Bergeron-Brlek
Office: TEL 2037
Office Hours: by appointment
e-mail: my e-mail

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.


(March 10, 2009) (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.

(March 10, 2009) I will be available only a short time before the quiz on Thursday. I will be in my office TEL 2028 from 1:30pm to 2:15pm (or shortly after 1:30pm since I have a class on the other side of campus). I will also respond to email questions (but refer to RULE #1).

(March 18, 2009) I had a mistake on the schedule and I placed one of the quizzes on Passover (a day when no exams are to be held). Since I spent an hour with the 'important dates' schedule in front of me setting the quiz dates in advance I don't know how this happened. I hav moved quiz 3 and quiz 4 and quiz 5 each forward by one lecture so this works out a little better for timing anyway (I didn't like that there were 5 lectures between quiz 2 and quiz 3).

(March 20, 2009) Anouk will have office hours on Wednesday 4-5pm. I will have office hours Tuesday 12-1pm.

(April 5, 2009) I added a few links about some recent news stories related to cryptography. If you see any current events that you think might be relevant to this class please pass them along because I would like to keep a record of what is going on during the semester.

(April 7, 2009) Here is the Monty Hall Problem page that we wrote ages ago.

(April 8, 2009) If you are interested in doing some programming projects for 'extra credit,' a couple of ideas that I would like to have done:
implement the algorithm described in the Diaconis paper in a Java applet (perferably using triple letter statistics rather than double letter statistics).
I am also interested in implementing a 'cryptography ladder' consisting of a sequence of puzzles (perhaps ever changing). For example, level one might be Ceasar, second might be Vigenere, third might be rectangular transposition, fourth monoalphabetic, fifth Vigenere/rectangular combination, etc.

(April 10, 2009) Note that there is an (intentional) error in the last problem on the practice for the 3rd quiz. We talked about it in class and the error is part of the problem. Also on the practice for the 4th quiz H( X x Z ) means 'the entropy of the random variable which you have recorded the value of X times the value of Z.' This problem as well as the first problem which appears on that practice quiz are the type of thing that I can ask you about entropy on Tuesday.

(April 20, 2009) I sent out the computer assignment by email. If you did not get a copy then see me. The assignments are due by April 28, 2009 and you may bring them to class or drop them off at my office before then. Remember, I am looking for just the keys and the passcode (please don't bring me pages of text).

(April 28, 2009) The exam schedule has been announced and the exam for this course will be May 29, 2009 from 7-10pm and will be held in SLH E (Stedman Lecture Hall next to York Lanes). More details will be announced as they are available.

(May 12, 2009) Course evaluations for this class are very important. They are done online and you should be getting email requests to fill them out from the registrar's office. In general the response rate for most classes is terrible and so I am making part of the final (3 points) if you have filled out an evaluation form. You must do it by MAY 21. Please provide comments as the forms allow because these comments help me to improve the course for next time.
Course evalations are at:

(May 20, 2009) Both the TA and I will be going out of town before the final and we will be unable to meet you in the week before the exam. I will have office hours Friday, May 22 from 1pm - 3pm. We will be able to answer questions over email.

(May 20, 2009) No smart phones will be allowed in the final. I found someone on the last quiz using their iPhone to calculate the gcd. Until tools like this become widely available you are to use +,-,*,/,^ and log on a calculator and not more advanced functions like factor, gcd, Jacobi, mod and discrete log which will all be possible within the next 5 years or so (if they are not now). 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 about the rest when we have tests and quizzes.

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.

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