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
April 30: Final paper draft due
April 29: Homework 14 due
April 22: Fully Homomorphic Ring-LWE Encryptiong
-
Read §5.4.3-4 of the online notes
April 20: Symmetric and Asymmetric Ring-LWE Encryption
- Read the solutions to homework 12
- Read §5.4.1-2 of the online notes
April 15: A New Hope Ring-LWE Encryption
- Homework 12 due
- Read §5.3.3-5.3.5 of the online notes
April 13: Rings and Learning with Errors
- Read §5.3.1-5.3.2 of the online notes
April 8: Lattices and cracking the Subspace Sum
-
Read §5.2 of the online notes
- See also §6.4-5 of HPS.
April 6: Subspace Sums and Post-Quantum Cryptography
- Read the solutions to homework 10 (Posted 1 AM April 6)
- Read §5.1 of the online notes
- See also §6.2 of HPS.
April 1: Shor’s Algorithm
-
Read §4.4 of the online notes
- See also Chapter 3, sections C and E of Lecture Notes on Quantum Computation by David Mermin
March 30: Setting up your Quantum Computer
- Read the solutions to homework 9.
- Read §4.3 of the online notes
- See also Chapter 2, section A and Chapter 3, section D of Lecture Notes on Quantum Computation by David Mermin
March 25: Complex Vector Spaces and Quantum Computers
- Homework 9 due
- Read §4.2 of the online notes
- See also Chapter 1, sections C-E of Lecture Notes on Quantum Computation by David Mermin
March 23: Classical Computers and Reversible Operators
- Read the solutions to homework 8.
- Read the Paper Description and Rubric and start thinking about your paper topic.
- Read §4.1 of the online notes
- See also Chapter 1, sections A-B of Lecture Notes on Quantum Computation by David Mermin
March 11: Elliptic Curve Cryptography
- Homework 8 due
- Read §3.8 of the online notes
- See also §5.2-4 of HPS
- Read the midterm solutions
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
- Homework 9 due Thursday, March 25
- Homework 10 due Thursday, April 1
- Homework 11 due Thursday, April 8
- Homework 12 due Thursday, April 15
- Homework 13 due Thursday, April 22
- Homework 14 due Thursday, April 15
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
Final Project
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.