January 26: Block Ciphers and the Hill Cipher
January 19: Polyalphabetic ciphers
- Read section 1.2-1.3 of the online notes
- See also §4.2 of HPS
- Numberphile Videos
- Paper Enigma
January 14: Cryptanalysis of Monoalphabetic Ciphers
- Fill out this survey about your background coming into the course.
- Finish §1.1 of the notes or of HPS.
January 12: Syllabus and Intro to Encryption
Cryptography is the study of sending secret messages over insecure communication channels. Cryptographic capabilities are important to politics and foreign affairs, and underlie the functioning of a great deal of the modern economy.
Unlike many math courses, this course will be oriented around a problem we’re trying to solve, rather than around a set of techniques. We’ll draw on basic ideas from fields including combinatorics, information theory, probability theory, number theory, geometry, and algebra to encrypt messages so they can’t be intercepted, and to break encryption schemes and interpret those secret messages sent by others.
In this course we will:
- Understand the mathematical underpinnings of cryptographic systems and be able to analyze their security.
- See how a problem-centric approach brings many different ideas and fields of math together to solve problems.
- Practice communicating mathematical ideas in writing and in oral communication, and translating technical mathematical ideas for a lay audience.
- Relate your mathematical knowledge of cryptographic systems to newsworthy events and policy issues.
The course syllabus is available here.
- Course Notes
- Other Resources
I will be basing much of this course off material from the book An Introduction to Mathematical Cryptography by Hoffstein, Pipher, and Silverman. This book seems to be freely available with your GWU login, so please go download the PDF from the above link. However, you should not ever need access to the book.