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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 and Key Exchange
  • Week 6: Public Key Cryptography
  • Week 7: Elliptic Curves
  • Week 8: Elliptic Curve Cryptography
  • Week 9: Knapsack Encryption
  • Week 10: Ring Learning with Errors

Homework

Final Presentation

Schedule:
  • November 9
    • Tristan Boblet (Hashing Functions)
    • Lyra Yu (Pseudorandom number generators)
    • Dylan Jirsa  (Zero-knowledge proofs)
    • Jay (Coding theory)
  • November 16
    • Katie Begerow (DES)
    • Shuyu Ding (Digital Signatures)
    • Sara Packer (Cryptocurrencies)
    • Elliott Smith (Steganography)
  • November 30
    • Ian Li
    • Eva Wang (KRACK)
    • Sherry Hou (real-world vulnerabilities

 Prompt

Potential topics:
  • Pseudorandom number generators (Lyra Yu)
  • Hashing functions (Tristan Boblet)
  • Coding theory
  • Collision attacks
  • Sources of real-world vulnerabilities (Sherry Hou)
  • I’d love for someone to explain the KRACK attack that broke Wifi this week (Eva Wang)
  • DES block cipher (Katie Begerow)
  • Primality testing
  • More on elliptic curves
  • More on lattice-based cryptography
  • Digital signatures (Shuyu Ding)
  • Zero-knowledge proofs (Dylan Jirsa)
  • Man-in-the-middle attacks
  • Cryptocurrencies (Sara Packer)
  • Error-correcting codes
  • Coppersmith attacks on RSA
  • Other