Mathematics of Cryptography
Math 4161 3.0
Tuesday, Thursday 2:30-4pm    CB 115
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
(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:
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
(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
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.