Mathematics of Cryptography
Winter 2010 - Math 4161 3.0
Tuesday  2:30-4pm  TEL 0007,     Thursday  2:30-4pm  TEL 0005
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
(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:
(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
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.