Syllabus for Cryptology: the Science of Secret Messages
First Year Seminar -- Fall 2004
Hentschke 204
Dr. Tamara Veenstra

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. We will study a variety of mathematical topics (matrices, modular arithmetic, probability and statistics, etc) as necessary to understand these codes.

Texts: Thomas Barr “Invitation to Cryptology” AND
Simon Singh “The Code Book”

Technology: We are likely to use some computer programs. Some assignments will be due over email. HW assignments are posted on my web site.

Topics and Approximate Schedule
We will spend 2-4 weeks on each of the four units:

• Unit 1: Monoalphabetic ciphers, implementing monoalphabetic ciphers with modular arithmetic, and using statistics to break these codes
• Unit 2: Polyalphabetic ciphers, Vigenere cipher, and Cryptanalysis of these ciphers especially Friedman and Kasiski test
• Unit 3: Block Ciphers – the Hill cipher, Playfair and DES, and various issues currently surrounding cryptography, translating messages to strings of numbers (arithmetic in base 26, binary, etc)
• Unit 4: Public Key Cryptography -- RSA, Diffie-Hellman, Digital Signatures, El Gamal.

Grading: Your grade will be based on the following categories: attendance/participation (5%), homework ( 30% ), quizzes and tests (50%), and a final project (15%).

Attendance and Participation: Active participation is required for this course. Homework: Homework assignments will consist of daily problem sets and weekly writing assignments. In addition to turning in daily homework assignments, some days you will also be responsible for presenting them on the board at the beginning of class. Writing assignments may relate to either the material in the course or involve questions related to your first year experience (or both) and will usually be due electronically.

Quizzes and Tests: At the end of each unit there will be a test covering the material in that unit. There will be reading and other quizzes throughout.

Final project: There will be a project where you explore, write a paper on, and present an additional topic in cryptography (of your choosing). You may work on these either individually or in pairs. These will be presented to the class during the final exam period and during the last week of class.