Honors Topics in Math for the Liberal Arts: Cryptology

Instructor: Wesley Pegden (pegd[*remove*this*]en@math.rutgers.edu)
Meetings: Tuesday and Friday, 9:50-11:10 (am), room 112 in Murray Hall
Textbook: Invitation to Cryptology, by Thomas H. Barr
Grade Breakdown: 40% Homework/Quizzes/Tests, 20% Midterm, 40% Final.

This course covers the mathematics of communicating secrets. We will discuss encryption schemes used thousands of years ago, as well as those used today in everyday communications. We will also discuss some of the public policy and political issues surrounding the use of cryptology, including media copy protection, electronic voting machines, and international and domestic surveilance. For a printer-friendly version of this information, download the syllabus.

Final Information

The final is Thursday, 5/7 from 12-3PM in Murray Hall 112 (the normal classroom for the course). Review material:
the Test
the Midterm
the Midterm review sheet (covering material since the test)
the Final review sheet (covering material since the Midterm.)

Note added for people that were not in this class: several assignments (especially on asymmetric systems in the latter part of the course) were conducted by email or in class and do not appear below.

First Homework

Due by Friday. Using the methods we discussed in class, break the code in this file, which contains a message encrypted with the Caesar cipher. To save you the trouble of counting letters, you can view the result of a letter count here. You DON'T have to decrypt the whole message, but just need to do enough to figure out where the passage is from (use google to identify the passage if you don't recognize it).

2nd Homework

Due by the beginning of class on Tuesday. Crack the second code from the affine cipher handout. The (mod 26) multiplication table will be helpful. Make sure to show your work for your solution. (If you email the solution, be sure to indicate what equations you solved to find the key). As usual, you just have to decrypt enough to identify the passage. If you have any trouble please email me.

3rd Homework

Due by the beginning of class on Friday, January 30. Crack the second code from the permutation cipher handout. As usual, you just have to decrypt enough to identify the passage. If you have any trouble please email me. The last codes from both the substitution and permutation sheets are good challenge problems. Reminder: there will be a quiz on Friday, covering the material we have talked about so far.

4th Homework

Due by the beginning of class on Friday, February 6. Crack the second code from the Vigenere cipher handout (this is the same one handed out in class). Start by finding the keyword length using the method we used in class (this is called the "Kasiki" test). Then choose the file that corresponds to what you think the keyword length is: 3, 5, 6, 8, 9, or 10. The file contains the letter count for each position relative to that possible keyword length, for you to use to break the code like we did in class. In your solution, you should give: what repeated words you used to find the keyword length (with their distances), the keyword the message was encrypted with, and the first line of the message (and where the message is from). Please email me if you have questions!

5th Homework

Due by the beginning of class on Friday, February 13. Crack the second code from the Hill cipher handout (this is the same one handed out in class). In class I gave the hint that the most common bigram in the text (ZU) corresponds to TH in the plaintext, while the fourth most common bigram (FJ) corresponds to HE in the plaintext.

Test on Tuesday, Feb 17

There will be a test on Tuesday, Feb 17, covering encryption, decryption, and "cracking" for all of the ciphers covered up till now. I recommend reviewing the worksheets already handed out (most have a ciphertext which was neither done in class nor assigned). I handed out a Vigenere cipher sheet with additional ciphertexts to review the techniques to break this encryption scheme. Note that some long repeated words are boldfaced to facilitate application of the Kasiki test. On Friday we also started to learn about binary, but this will not be on the test.

6th homework

Due Tuesday, Feb 24: 3a,3c,5,7 from page 220 in the book. This is the material on simple stream ciphers based on Linear Feedback Shift Registers.

7th homework

Due Friday, Feb 27: the last three problems from the stream cipher worksheet. These include LFSR-based stream ciphers where even the underlying LFSR formula is not known.

8th homework

Due Tuesday, March 3: read the BabyCSS handout on the BabyCSS cipher we covered in class on Friday, and do the exercises at the end of it. Note that the answers for 1a, 2a, and 2b are written at the bottom of the page; this is so that you can try those and check that you are doing the basic things right. (You should still write up and turn in these problems.) Please email me if you have any questions.

9th homework

Due Friday, March 10: read chapter 5 (the farmers' tale: an allegory) from the book "The Public Domain: Enclosing the Commons of the Mind". This book is $18.81 on Amazon.com, should be available at the Alexander Library (although its status says "In-Process"), or can be downloaded as a free pdf from the book's website.

10th homework

Due Friday, March 17: Do exercise 2 from the sheet of BabyBlock ciphers. The handout from class may be helpful. Each of the ciphers 4-6 (those using cipherblock chaining) can be done for 1 bonus point each, to be added to your overall homework grade.

Midterm/group projects

Group presentations are on Tuesday March 24, and the Midterm is on Friday March 27. The review sheet is good preparation for the midterm. Don't forget to review the test!

11th homework

Due Tuesday, April 7: Do the problems from the gcds and inverses using the Euclidean and Extended Euclidean algorithms. As discussed in class, you also need to setup yourself to send and receive encrypted email using GPG, and succesfully exchange encrypted emails with the instructor.