Mathematics of Cryptography

Math 4161 3.0
Tuesday, Thursday 2:30-4pm    CLH M

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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: Mondays or Wednesdays before the quiz
e-mail: my e-mail


Raw grade scores for all class grades have been posted under the last 4 digits of your student id. Please check your scores ASAP and let me know if there are any discrepencies.

Operations resume at York on Monday

TORONTO, December 16, 2007 -- York University will resume normal operations on Monday, December 17, 2007.
Check the weather status page for updates at:

This means that the exam for math 4161 is on as scheduled. It will be held at 9am-12pm in SLH E.

There is a problem on the third practice final with the Feistel cypher question that has an 8x8 table (it is labeled question (1)). The 8x8 table should be a 16x16 table in order for the problem to work correctly. The question works better if in part (a) (L,R) = 110 001 and K = 011 and in part (b) (L,R) = 011 111 and K = 100.

I had reserved a room for the problem session but it turns out it was already booked. My bad. The room next to the undergraduate math office and the elevators in the north tower is called the 'common room.' This has been reserved for the problem session. Sorry for any confusion.

The question on ElGamal in the second practice is slightly strange because one would assume that since Alice is sending the message, Y should be equal to 19. For the purposes of ElGamal, assume that Alice is using a different private/public key than she used in the previous problem but that Bob is using the same private/public key.

Those of you who have gotten an early start on the practice questions and have questions to ask can attend the TAs office hours. Anouk will be available Thursday December 6 from 10-11:30am. I am still planning to hold a problem session on Friday December 14 from 1-3pm. I have not reserved a room for this. Be aware that there will not be enough time to cover all of the practice problems that I gave you during the problem session so come prepared.

I have posted the computer assignments on the page with the grades. 3 people gave me quizzes to regrade from quiz 7 and I will bring those on Thursday because I don't have them with me today (Tuesday Nov 27).

The final exam is not comprehensive. It will only cover the material that we do during the last few weeks of class (except for perhaps a bonus problem which could come from any point in the course). I expect that the final exam should be roughly the length of two quizzes. I will post a practice for the final before the end of next week.

I completely miscalculated the number of classes that we had left because I thought that we had classes during the first week of December. What this means is that we will have only 7 quizzes (like that isn't enough) because if we use the remaining hour for another quiz then I won't be able to cover some really interesting stuff we have left. You still will be able to drop the lowest two quizzes.

I got the following message from the mathematics department. I know that we did in class evaluations but if you like filling out evaluation forms I am always looking for more feedback to make this course better:
The Fall 2007 Course evaluations are now available on-line. The URL link is

Students with valid email addresses should have received notice that they should go on-line and complete the course evaluations. Students have from November 14 to December 4 to submit the evaluations. Weekly reminders are also being sent out to those who have not yet completed them.

Please encourage and remind your students to go on-line and complete the course evaluations. If you have any questions or require additional information, please let me know.

Late announcement: Quiz 7 is on Tuesday the 20th, Anouk will hold office hours on Monday the 19th 2:30-4pm and I will hold office hours 12-1 on Tuesday the 20th.

I sent out the computer assignment. In the email I gave you a file that was encrypted first with rectangular transposition and then with Vigenere. You should be able to use the applets which are posted on the handout section of the website to recover the message. Please hand in a page with ONLY the three things that I asked for before November 15th. If you did not receive the computer assignment by email then please send me an email with your full name.

I moved the 6th quiz to November 13th. The TA will hold office hours from 2:30-4 on Monday November 12th.

The 5th quiz is on November 1, 2007. The TA will hold office hours on Monday October 31 from 2-3:30pm.

The 4th quiz may not be ready by class on October 30th. I posted the 4th quiz in the handout section consider it as practice for quiz 5 too since it involves a lot of entropy.

Next quiz is on October 16, 2007. The TA will hold office hours on Monday October 15 from 2:30-4pm. Look for a practice quiz in the handouts.

Next quiz is on October 2, 2007. The TA will hold office hours on Monday, October 1 from 2:30-4pm.
There will be a quiz on Thursday September 20. The TA will hold office hours on Wednesday September 19, 2-3:30pm and I will hold office hours Thursday Septemeber 20, 12-1pm.

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.

Text : This year I have decided to not require a text for the course. The reason is that the last time that I taught the class we follwed the 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 then I suggest that you search this book out, but the notes will prove to be more useful. 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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