Math 4981: Cryptography
Spring 2021

Contact Info
Spring 2021

Office: Blackboard

Office Hours:

Course Information


Official textbook:

Daily Assignments

March 11: Elliptic Curve Cryptography

March 9: Elliptic Curves over the Rationals

March 4: Intro to Elliptic Curves


March 2: Breaking RSA


February 25: Public Key Encryption: ElGamal and RSA


February 23: The Discrete Logarithm


February 18: Diffie-Hellman Key Exchange


February 16: One-Way Functions, Coding, and Key Exchange


February 11: Complexity


February 9: Secrecy, Entropy, and Unicity Distance

I accidentally lost the slides from today’s lecture, sorry. You can still see the lecture video on blackboard.

February 4: Perfect Secrecy


February 2: Probability


January 28: Modules and the Hill Cipher


January 26: Block Ciphers and the Hill Cipher


Important: Blackboard crashed for me, and at least some other people, during class today. We moved over to Discord to finish the course, but with the difficulties we only got through 1.4.2 and didn’t cover 1.4.3, which we’ll be talking about on Thursday.

I’m also going to do a quick recording of that portion of the lecture once Blackboard comes back up, hopefully tonight, so if you missed the Discord lecture you can still see a version of it.

Apologies for the technical problems; I don’t know what happened but I hope it won’t happen again. If it does, we’ll probably just move to Discord again so check there.

January 21:


January 19: Polyalphabetic ciphers


January 14: Cryptanalysis of Monoalphabetic Ciphers


January 12: Syllabus and Intro to Encryption


Course Goals

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:

The course syllabus is available here.

Course notes



Final Project

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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.