# Math 4981: Cryptography Spring 2021

#### Contact Info Spring 2021

Office: Blackboard
Email: jaydaigle@gwu.edu

Office Hours:

#### Course Information

Lecture:

• TR 11:10 AM–12:25 PM
• on Blackboard

Official textbook:

## Daily Assignments

#### May 4: Final Exam Due

• Final Exam due midnight on Tuesday, May 4
• Final study guide:
• Elliptic curves
• Elliptic curve cryptography
• Quantum computers
• QFT and Shor’s algorithm
• Knapsack encryption
• ANH encryption
• SHE encryption

Slides

Slides

Slides

Slides

Slides

#### April 6: Subspace Sums and Post-Quantum Cryptography

Slides

• Read the solutions to homework 10 (Posted 1 AM April 6)
• Read §5.1 of the online notes

Slides

Slides

Slides

Slides

Slides

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

Slides

• Midterm due
• Midterm study guide:
• Caesar Cipher
• Monoalphabetic Cipher
• Vigenère Cipher
• Autokey Cipher
• Hill Cipher
• Probability
• Entropy
• Diffie-Hellman
• ElGamal
• RSA
• Read the rest of §3.7 of the online notes
• Read the solutions to homework 7.

Slides

Slides

Slides

Slides

Slides

Slides

Slides

#### 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.

Slides

Slides

Slides

#### January 26: Block Ciphers and the Hill Cipher

Slides

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)
• Read the solutions to homework 1.

Slides

Slides

#### January 14: Cryptanalysis of Monoalphabetic Ciphers

Slides

• Fill out this survey about your background coming into the course.
• Finish §1.1 of the notes or of HPS.

Slides

## 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.

## 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 Exam due midnight on Tuesday, May 4
• Final study guide:
• Elliptic curves
• Elliptic curve cryptography
• Quantum computers
• QFT and Shor’s algorithm
• Knapsack encryption
• ANH encryption
• SHE encryption

## 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.