This course is an introduction to the theory of cryptography and cryptoanalysis.

News (Last Updated: Dec 16, 2013)

Below is a summary of what we did in class, plus any relevant news and/or information.

• Dec. 16 I have submitted the final marks. Good luck with the rest of your exams, and all the best in the new year!
• Nov. 18 Tuesday will be the last lecture for this courses (given by Dr. Lee). You will look at some additional topics of RSA cryptography (e.g. signature exchange). I have also added a review sheet for the final exam. Continue to work on your homework and project.
• Nov. 11 This week Dr. Lee will teach the material on RSA cryptrography. See the email I sent to the class on what topics you should understand. Continute to work on your homework and project.
• Nov. 4 This week, Dr Dean and Lee will help cover the lecture material. The focus this week is the mathematics behind the public-key encryption system called RSA. You will learn the material from Section 4.1, and learn some of the properties of a public-key encryption system.
• Oct. 29 This week Dr. Liu will cover the remaining material of Chapter 3. In particular, she will explain the Hill encryption system. Also, she will show you how to use a spreadsheet to help with your calculations. NOTE: Because class was cancelled last week, I have now pushed back all the assignments to the next class. They will now be due on Tuesdays, instead of Thursdays.
• Oct. 24 Dr. Lee taught Section 3.1 on matrices. You should know how to determine if a matrix is invertible if its entries belong to Z_26.
• Oct. 22 Class was cancelled.
• Oct. 17 Today was our midterm. It will be returned on Tuesday (along with HWA 4).
• Oct. 15 Today we started Chapter 3. We looked at two simple examples of a polygraphic substititon cipher. The next class will be our midterm. You can pick up HWA 4 in my office.
• Oct. 10 In today's class, we finished our discussion of the cryptoanalysis of the Vigenere Cipher. I handed back HWA 3, and collected HWA 4. Just a reminder that next week is the midterm. A review sheet is on the web (look to the right).
• Oct. 8 We looked at Section 2.5 on how to decrypt a Vigenere cipher. You should know how to find the length of a keyword.
• Oct. 5 I placed a revised project overview on the web. As I mentioned in class, if you would like to code, this is now an acceptable project. The project overview sheet has been updated to reflect this fact. I will also send a link to a Google Docs to enter in your project information.
• Oct. 3 In today's class we started our discussion of Section 2.5 on disguising frequencies using polyalphabetic substitution ciphers. I handed back HWA 2, and collected HWA 3.
• Oct. 1 Today we went over Sections 2.3 and 2.4. Like the material on last Thursday, the majority of this material was review.
• Sept. 26 Today we finished up Section 1.6 (we went over the solution of the problem given on Tuesday), and we looked at Sections 2.1 and 2.2. (Note: we had no formal lecture on this material, but you are expected to know it). I handed back HWA 1, and collected HWA 2.
• Sept. 24 We looked at Section 1.6 today; after today's class, you should be able to decipher a text that was encoded using an additive, multiplicative, or affine cipher. Also, the textbooks should be in the bookstore later today.
• Sept. 19 In today's class, I introduced four encryption schemes: additive, multiplicative, affine, and keyword. See Section 1.5 of the text for more. HWA 2 is on the web and HWA 1 was due in class.
• Sept. 17 We went over Sections 1.3 and 1.4. You should know the Fundamental Theorem of Arithmetic and how to use modular arithmetic.
• Sept. 12 Today we went over Section 1.2 on the Euclidean algorithm. Make sure you download HWA 1 -- it is due next week Thursday.
• Sept. 10 First day of classes! Today, we went over the course outline, and we covered Section 1.1 of the text. Please read 1.2 and 1.3 for Thursday.
• Sept. 2 Some minor changes, including office hours.
• Aug. 12 I have updated the course webpage with more content about the course. In particular, the course outline has been added.
• Jul. 24 Not much to see yet! Getting the webpage set up for the fall.

Useful Websites

• Cryptological Mathematics
  The website companion for our textbook. There are some software programs you can download (for Windows only).
• Wolfram Alpha
  A go to website for all sorts of computations!
• Character Frequency Analysis
  A website that counts character frequency, as well as digraph frequency.
• Index of Coincidence
  A website that allows you to compute the I.C., as well as some discussion on this invariant.

Text Book and Original Sources

• Cryptological Mathematics
  by Robert Edward Lewand

• Purchase from the internet
• Purchase a copy from Lakehead's Bookstore.

• L. Hill, Concerning certain Linear Transformation Apparatus of Cryptography. American Mathematical Monthly (1931) 135-154
• R. L. Rivest, A. Shamir, L. Alderman, A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21 (1978) 120--126.

Text for project

It is a truth universally acknowledged that a single man in possession
of a good fortune must be in want of a wife

However little known the feelings or views of such a man may be on his
first entering a neighbourhood this truth is so well fixed in the minds
of the surrounding families that he is considered the rightful property
of some one or other of their daughters

My dear Mr Bennet said his lady to him one day have you heard that
Netherfield Park is let at last

Mr Bennet replied that he had not

Instructor: Adam Van Tuyl

Office: Ryan Building 2015
Office Hours: TWTh 2:30-3:30
Email: avantuyl AT lakeheadu.ca

Place and Time:

Class: TTh 8:30-10:00 in Ryan Building 2047

Textbook:

Cryptological Mathematics
by Robert Edward Lewand

Homework is given out every Thursday, and will be due, at the beginning of class, the following Thursday. Assignments must conform to the guidelines in the course outline. Assignments are posted below.

Assignment 1 (Due: Sept 19)

Assignment 2 (Due: Sept 26)

Assignment 3 (Due: October 3)

Assignment 4 (Due: October 10)

Assignment 5 (Due: October 22) [NOTE DATE!]

Assignment 6 (Due: November 5)

Assignment 7 (Due: November 12)

Assignment 8 (Due: November 19)

Assignment 9 (Due: November 26)

All class handouts are available as PDF files.

Course Information
Course handout from first day of class

Presentation Information REVISED: OCT 5
Handout describing course project

Midterm Information
Review sheet for midterm.

Final Exam Information
Review sheet for final exam.

Homework = 15%
Midterm = 25%
Project =15%
Final Exam = 45%

Sept. 9, 2013
First semester classes begin

Oct. 14, 2013
Thanksgiving (no class)

Oct. 17, 2013
Midterm 1

Oct. 17, 2013
Project topic due

Nov. 19, 2013
Written project due

Nov. 19,21,26, 2013
Presentations

Dec. 2, 2013
First semester classes end

Dec. 5-17, 2013
Exam period

Lakehead University

LU Math Department

Adam's Home Page

Student Code of Conduct