Course Goals
- 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.
You can find a link to the syllabus here.
Notes
- Week 1: Intro to Cryptography
- Week 2: Cryptanalysis
- Week 3: Block Ciphers
- Week 4: Information Theory
- Week 5: Discrete Logarithms
- Notes
- No Slides
- Week 6: Public Key Encryption
- Notes
- No Slides
- Week 7: Elliptic Curves
- Week 8: Elliptic Curve Cryptography
- Week 9: Knapsack Encryption
- Notes
- No Slides
- Week 10: Ring Learning with Errors
- Notes
- No Slides
Homework
- Week 1, due Thursday September 6
- Week 2, due Thursday September 13
- Week 3, due Thursday September 20
- Week 4, due Thursday September 27
- Week 5, due Thursday October 4
- Week 6, due Thursday October 11
- Week 7, due Thursday October 18
- Week 8, due Friday October 26 at 4 PM in my office
- Week 9, due Thursday November 1
- Week 10, due Thursday November 15
Final Presentation
Schedule:
- November 8
- Jay Daigle (DES)
- Vena Zhang (Pseudo-Random Number Generators)
- Andrew McCall (Digital Signatures)
- Silvia Yang (Hash Functions)
- November 15
- Luis Figueroa (Cryptocurrencies)
- Myriam Segura (Coppersmith)
- Jimmy Li (Collision Attacks)
- Suzette Reyes (Man in the Middle Attacks)
- November 29
- Andrew Poggione (Error-Correcting Codes)
- Paige Waters (Coding Theory)
- Bryan Smith
- Sophia Vallas (Zero-Knowledge Proofs)
Potential topics:
- Pseudorandom number generators (Vena Zhang)
- Hashing functions (Silvia)
- Coding theory (Paige Waters)
- Collision attacks (Jimmy Li)
- Sources of real-world vulnerabilities
- Pick a specific recent hack and explain how it works
- DES block cipher (Jay)
- Primality testing
- More on elliptic curves
- More on lattice-based cryptography
- Digital signatures (Andrew McCall)
- Zero-knowledge proofs (Sophia Vallas)
- Man-in-the-middle attacks (Suzette Reyes)
- Cryptocurrencies (Luis Figueroa)
- Error-correcting codes (Andrew Poggione)
- Coppersmith attacks on RSA (Myriam Segura)
- Other