Mathematics of Cryptography

Winter 2012 - Math 4161 3.0


Tuesday,     Thursday  2:30-4pm  TEL 1005

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Professor Mike Zabrocki
Office: TEL 2028
Office Hours: April 2, 5-6pm; April 9, 16 at 3-4:30pm
e-mail : my e-mail
web page: http://garsia.math.yorku.ca/~zabrocki
course web page: http://garsia.math.yorku.ca/~zabrocki/math4161w12/


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 and the mathematics that is used in modern cryptography.


Announcements:

(January 3, 2012) (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 11, 2012) It turns out that there are some electronic clicker apps out there and I have three or four upcoming activities where they would be useful. I've checked out one and want to put it into use. If you are interested in participating and you have a laptop, Android or Apple smartphone, iPad, Kindle, or other electronic device for reaching the internet then please bring it to class on Jan 17 and 19. The website for the clicker is http://m.socrative.com and there is an app for Android and iPhone/iPad that you can find by searching for 'socrative' (you will want the student app and not the teacher app). The 'room number' for my courses is 12748 .

(January 11, 2012) The first quiz won't be ready to hand back until Jan 17.

(January 11, 2012) I made this announcement the first day of class but forgot to post it on the website:
Please make an announcement in your classes regarding the upcoming Mathematical Contest in Modeling (MCM). The MCM is a contest where teams of undergraduates use mathematical modeling to present their solutions to real world problems. Each team can have a maximum of three members who work together to find a solution to one of three posed problems. The solution may include mathematics as well as computer simulation. The team must also write a report on their solution. Problems are designed to be open-ended and are unlikely to have a unique solution. Attention must be focused on clarity, analysis, and design of the solution.

The MCM will take place on February 9-13, 2012. If students have any questions regarding the MCM they may email me (jmheffer@mathstat.yorku.ca) or look at the MCM website http://www.comap.com/undergraduate/contests/. If they are interested in participating they should email me by Jan 15. There will be an information/training session in late January.


(January 11, 2012) My colleage and I are in need of a linux guru for some work this coming summer. If you think that you or someone you know is interested please have them contact me and we can set up a meeting.

(January 11, 2012) The National Science and Engineering Research Council of Canada/Conseil de recherches en science naturelles et en génie du Canada (NSERC/CRSNG) has a research award program for students to work part time during the summer. These awards are highly comptetitive and if you are interested you should apply. Information on the program is available here : http://www.nserc-crsng.gc.ca/Students-Etudiants/UG-PC/USRA-BRPC_eng.asp

(March 31, 2012) I updated office hours for finals week. I will have office hours on Monday April 2, 5-6pm; April 9, 16 at 3-4:30pm.

(April 2, 2012) I have posted a copy of the quiz grades that I have for you at this link here. They are sorted by the last 4 digits of your student id number. The last column represents the sum of the normalized quizzes (quizzes 1,3 and 5 were out of 32, quizzes 2 and 4 were out of 24) with the lowest grade thrown out. Please check that these grades agree with your records.



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. 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 one 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 currently 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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