## Daily Assignments

#### March 11: Elliptic Curve Cryptography

- Homework 8 due
- Read §3.8 of the online notes
- See also §5.2-4 of HPS

#### March 9: Elliptic Curves over the Rationals

- Midterm due
- Midterm study guide:
- Caesar Cipher
- Monoalphabetic Cipher
- Vigenère Cipher
- Autokey Cipher
- Hill Cipher
- Probability
- Entropy
- Diffie-Hellman
- ElGamal
- RSA

- Midterm study guide:
- Read the rest of §3.7 of the online notes
- See also §5.1 of HPS, again.

- Read the solutions to homework 7.

#### March 4: Intro to Elliptic Curves

- Homework 7 due
- Read §3.7 of the online notes, up through “Geometry and the Group Law”.
- See also §5.1 of HPS

#### March 2: Breaking RSA

- Read §3.6 of the online notes
- See also §3.3 and §3.5 of HPS

- Read the solutions to homework 6.

#### February 25: Public Key Encryption: ElGamal and RSA

- Homework 6 due
- Read §3.4-5 of the online notes
- See also §2.4 and §3.2 of HPS.

#### February 23: The Discrete Logarithm

- Read §3.3 of the online notes
- See also §2.2 of HPS.

- Read the solutions to homework 5.

#### February 18: Diffie-Hellman Key Exchange

- Homework 5 due
- Read §3.1-2 of the online notes
- See also §2.1 and §2.3 of HPS

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

- Read §2.4 of the online notes
- See also §1.7.2

- Read the solutions to homework 4.

#### February 11: Complexity

- Homework 4 due
- Read §2.3 of the online notes
- See also §4.7 of HPS

#### 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.

- Finish §2.2 of the online notes
- See also §4.6 of HPS

- Read the solutions to homework 3.

#### February 4: Perfect Secrecy

- Homework 3 due
- Read §2.2 of the online notes (Up[dated 8:30 PM on Feb 6)
- See also §1.7.1 and §4.6 of HPS

#### February 2: Probability

- Read §2.1 of the online notes
- §4.3 of HPS

- Read the solutions to homework 2.

#### January 28: Modules and the Hill Cipher

- Homework 2 due
- Finish §1.4

#### 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.

- Read section 1.4 of the online notes (2AM Jan 26)
- See also §1.7 in HPS.

- Read the solutions to homework 1.

#### January 21:

#### 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

- Please read the syllabus
- Read one of
- Section 1.1 of the online notes
- HPS §1.1.

## 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:

- 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

- Course Notes
- Other Resources

## Homework

- Homework 1 due Thursday, January 21
- Homework 2 due Thursday, January 28
- Homework 3 due Thursday, February 4
- Homework 4 due Thursday, February 11
- Homework 5 due Thursday, February 18
- Homework 6 due Thursday, February 25
- Homework 7 due Thursday, March 4
- Homework 8 due Thursday, March 11

## Midterm

- Midterm due midnight on Tuesday, March 9
- Midterm study guide:
- Caesar Cipher
- Monoalphabetic Cipher
- Vigenère Cipher
- Autokey Cipher
- Hill Cipher
- Probability
- Entropy
- Diffie-Hellman
- ElGamal
- RSA

## Final Project

lorem ipsum

## Textbook

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.