Cryptology and number theory (Math 5248)

Instructor: Igor Pak
pak@umn, 5-3855

Class schedule: TuTh 2:30 - 3:55, VinH 113

Office Hours: MW 2-3:30, room VinH 258

Grader: TBA

Textbook: Lecture notes are available from Alpha Print

Additional reading will be handed out in class if necessary.

Grading: Homeworks: 30%, Two Midterms 20%, Final 30%

Difficulty: 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.

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.


The topics covered will be similar to when the course has been taught in the past by Prof. Paul Garrett, the author of our text (see Vic Reiner's old syllabi). There are a lot of useful things on Garrett's crypto page, including his transparencies from his own lectures.

Other introductory textbooks (where further examples can be found)
Johannes Buchmann, "Introduction to Cryptography", Springer
Richard A. Mollin, "An Introduction to Cryptography", CRC Press
Douglas Robert Stinson, "Cryptography: Theory And Practice", CRC Press
Wade Trappe, Lawrence C. Washington, "Introduction to Cryptography: With Coding Theory", Pearson Prentice Hall

Home Assignments

The weekly home assignments will be given on Tuesdays to be returned also on Tuesdays, starting Sep 11 (due Sep 18). No assignment will be given over Thanksgiving break or concurrently with take home midterms. The assignments will be posted here (on the course web page) in .ps and .pdf format.

Homework 1. Download .pdf file.

Homework 2. Download .pdf file.

Homework 3. Download .pdf file. See Luhn algorithm Wikipedia article. See also .pdf file of the patent.

Homework 4. Download .pdf file.
Here is the answer to one of the midterm problems.
Here is where the "A snapshot in the family album" sentence came from.
More on RSA. More on Crypto.

Homework 5. Download .pdf file.

Homework 6. Download .pdf file.

Homework 7. Download .pdf file.
Read this and this Wikipedia articles.

Midterm and Final Exams

There will be two midterms and one final, all take home. The schedule is: Oct. 4-9, Nov 1-6 and during the Finals week.

Midterm 1. Download .pdf file.

Midterm 2. Download .pdf file.

Collaboration Policy.

For the homeworks, you can form discussion groups of up to 5 people each. You can discuss problems but have to write your own separate solutions. You should write the list of people in you group on top of each HW.
Since the midterms and the final are all take home, no collaboration or consultation with other students (in fact, all other humans) is allowed. This will be strictly enforced. Of course, you are free to use any textbooks, web, etc.

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Last updated 9/4/2007