Mathematics of Cryptography
Winter 2012 - Math 4161 3.0
Tuesday,     Thursday  2:30-4pm  TEL 1005
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.
(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
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 (email@example.com) 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 :
(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
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.