Daily Assignments
April 22: Lattices and cracking the Subspace Sum

Read §5.4.34 of the online notes
April 20: Asymmetric RingLWE Encryption
 Read the solutions to homework 12 (not yet posted)
 Read §5.4.12 of the online notes
April 15: A New Hope RingLWE Encryption
 Homework 12 due
 Read §5.3.35.3.5 of the online notes
April 13: Rings and Learning with Errors
 Read §5.3.15.3.2 of the online notes
April 8: Lattices and cracking the Subspace Sum

Read §5.2 of the online notes
 See also §6.45 of HPS.
April 6: Subspace Sums and PostQuantum 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 CE 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 AB 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 §5.24 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
 DiffieHellman
 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 §3.45 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: DiffieHellman Key Exchange
 Homework 5 due
 Read §3.12 of the online notes
 See also §2.1 and §2.3 of HPS
February 16: OneWay 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 1.21.3 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 problemcentric 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 12 due Thursday, April 22
Midterm
 Midterm due midnight on Tuesday, March 9
 Midterm study guide:
 Caesar Cipher
 Monoalphabetic Cipher
 Vigenère Cipher
 Autokey Cipher
 Hill Cipher
 Probability
 Entropy
 DiffieHellman
 ElGamal
 RSA
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.