Math 5248: Cryptology and number theory

Fall 2004

Prerequisites: Calculus, linear algebra, and not much else.
Instructor: Victor Reiner (You can call me "Vic"). 
Office: Vincent Hall 256
Telephone (with voice mail): 625-6682
Classes: Monday, Wednesday, Friday 1:25-2:15pm
in Vincent Hall 113
Office hours: Monday and Wednesday 2:30-3:20 pm, Thursday 10:10 -11:00 am, and also by appointment.  
Course content: This is an introductory course in cryptology, that is, the subject of how to make ciphers (cryptography) and break them (cryptanalysis). The math used is heavy on modular arithmetic, which will be covered in some depth. It also makes some use of elementary counting and probability, plus a tiny bit of linear algebra and matrices. It is not intended as a substitute for a serious abstract algebra or number theory course.
One can get a more detailed sense of the topics covered by looking at the schedule of weekly topics, homeworks and exams; here it is in PDF , PostScript .
Note: Unlike previous years, when Paul Garrett (the author of our text) taught one big lecture of the course, this year it is taught in 3 separate lectures. However, we are sharing a common course structure, grading system, schedule of topics, homework structure, and exams. In many ways, the course will have a similar spirit to when Garrett last taught it, and so looking at his crypto page may be useful to you. However, note that we will definitely not be having a term project, and we definitely will be having a final exam during the usual exam week.
Text: Making, breaking codes: An introduction to cryptology by Paul Garrett, Prentice Hall 2001.
This should be available at the bookstore. Try to get the 2nd printing, which corrected some minor errors.
Errata found after 1st printing
Errata found after 2nd printing
For historical background:  The code book by Simon Singh
The code breakers by David Kahn
Homework: There will be weekly homework assignments, except for the 3 weeks with midterm exams, due at the beginning of each Wednesday class. Each student in my lecture will be given on the first day of class a "version number" in the range 101-150, and will be handing in their appropriately numbered homework assignments with individualized data. Here are those assignments for the whole semester in PDF , PostScript .
Late homework will not be accepted. Collaboration is encouraged as long as everyone collaborating understands thoroughly the solution, and you write up the solution in your own words. In addition, since each person's homework problems have individualized answers, you'll get the wrong answer if you simply copy!
Note: Homework problems that are not marked "short answer" are asking for an answer in clear English (with math symbols allowed), giving a careful and genunine explanation of how the problem is solved, not just, for example, a numerical answer. On these problems, imagine you are writing to a mathematically literate person who just happens not to know about the material or methodology behind that particular problem. Here you will be marked down for
  • hiding behind vague language
  • hiding behind phrases like "Obviously/Clearly ..."
  • relying too much on the fact that the grader knows the answer already and therefore should be able to figure out "what you meant" anyway
  • blathering on and on, rathering than focussing on the core issues concisely.
Exams and grading:  There will be three midterms exams in class on these three Wednesday classes:
October 13, November 10, December 8.
There will also be a two-hour final exam on Friday, December 17 at 1:30pm.
The grading in this course will not be curved.
Homework = 50% of grade
Each of 3 midterms = 10% of grade
Final exam 20% of grade.

A=93.00-100.0, A-=90.00-92.99, B+=86.67-89.99, B=83.34-86.66, B-=80.00-83.33
C+=76.67-79.99, C=73.34-76.66, C-=70.00-73.33, D+=65.00-69.99, D=60.00-64.99, etc
When grading in the S/N system, an 'S' is equivalent to a 'C' or better.
Complaints about the grading should be brought to me.

Some software:  Some Mathematica code for doing Vigenere encryption and the Friedman attack on it.
The example of this that was shown in lecture on Oct. 6, 2004.
Policy on incompletes:  Incompletes will be given only in exceptional circumstances, where the student has completed almost the entire course with a passing grade, but something unexpected happens to prevent completion of the course. Incompletes will never be made up by taking the course again later. You must talk to me before the final exam if you think an incomplete may be warranted.  
Other expectations  This is a 4-credit course, so I would guess that the average student should spend about 8 hours per week outside of class to get a decent grade. Part of this time each week would be well-spent making a first pass through the material in the book that we anticipate to cover in class that week, so that you can bring your questions/confusions to class and ask about them.

Back to Reiner's Homepage.