Contact Information:
Prerequisite: Math 122 or Math 121 and permission of the instructor. In particular, you should be comfortable with algebraic manipulations.
Texts: Singh's 'The Code Book' AND 'Kirtland's Identification Numbers and Check Digits'
Technology: We are likely to use some computer programs. Some assignments will be due over email. HW assignments are posted on my web site.
Course Objectives:
- to understand the mathematics involved in encrypting and decrypting information;
- to improve your problem solving abilities;
- to improve your ability to think logically, analytically, and abstractly; and
- to improve your ability to communicate mathematics, both orally and in writing.
Course Content:
In this course, we will study the mathematics behind encrypting and decrypting secret messages. We will primarily follow a historical approach, beginning with the simplest methods of encoding messages, and work up to some of the more complicated present day cryptographic systems, which are used in web and electronic security. We will also discuss methods of breaking these codes and which ones are secure. Mathematics has played an important role in developing and breaking codes. We will study a variety of mathematical topics (matrices, modular arithmetic and a bit of other number theory, and some probability and statistics) as necessary to understand these codes.
Schedule: We will cover approximately one unit per week.
Unit 1: Monoalphabetic and Polyalphabetic ciphers, and cryptanalytic attacks of these ciphers, (chapters 1 and 2 of Singh)
Unit 2: Check Digits and Error correcting codes (chapters 1&endash;2 of Kirtland), ENIGMA and the impact of technology on cryptography (chapter 3,4 of Singh)
Unit 3: Public Key Cryptography -- RSA, Diffie-Hellman, Digital Signatures, El Gamal (chapters 6-7 of Singh, Section 2.8 of Kirtland)
Unit 4: Block Ciphers &endash; the Hill cipher and DES, and various issues currently surrounding cryptography (ch 3 of Kirtland and various articles)
Grading: Your grade will be based on the following categories: attendance/participation (10%), daily homework and quizzes (30%), weekly papers (40%), and a final exam (20%).
Attendance and Participation: We will cover a lot of material in each 3-hour class session, and much of it is not in either of your texts. Thus attending each class period is imperative. Attendance will be taken each class period, but you will only receive credit for attendance if you are actively participating in class. Excused Absences: if you are sick, you may excuse your absence by contacting me before 2 pm on the day you miss class. (An email or phone message saying you are sick is all I need.) Any other absences must be excused in advance and require a significant reason. You are responsible for any material that is covered during your absence and must get and complete the homework assignment for the next class.
Daily Homework and Quizzes: You will be responsible for daily assignments. I will check these at the beginning of class and call on people at random to put them on the board. We will then discuss the problems. If you have made a significant effort on all the problems, you will get full credit for doing the daily HW. That is, you will be given credit based on evidence of effort regardless whether or not the problems are completely solved or solved correctly. Mathematics is best learned when you practice the material right away. Therefore, late homework is seriously discouraged and will be penalized at 25% per day. Homework will not be considered late if the absence is excused.
There will also be announced quizzes and/or pop quizzes based on the homework given throughout the term. Quizzes will be based primarily on the homework. (Unlike the HW, they will be graded on correctness rather than effort…)
Weekly Papers: These papers will either be questions based on assigned reading or summaries of the codes we have been discussing in class. As with any paper, I expect these to be well written. One of the goals for this class is for you to think about how to communicate effectively. You are strongly encouraged to find a friend who is willing to proof read your papers for you. (The writing center is also a good place for help here.) Presentation will be a significant portion of your grade on these, and poorly written papers will be returned to be rewritten (and penalized by one full letter grade.)
Papers and Due Dates (more specifics on these will be given later):
1. Due Jan 10: Reading paper based on chapter 1 of Singh. See attached sheet.
2. Due Jan 17: Summarize monoalphabetic and polyalphabetic ciphers as well as the methods used to break these codes.
3. Due Jan 21: Reading paper based on Ch 3,4 of Singh.
4. Due Jan 29: Summarize Public Key Cryptography.
Final Exam: There will be a final exam on Feb 2.
Academic Honesty Policy: Academic honesty is expected of all students. You should read this policy in the catalog. Specifically, you are encouraged to discuss any material in this class with your peers. However, all write-ups (HW, papers) and tests should be your own work.