CO 485/685 - Fall 2009

The Mathematics of Public Key Cryptography

Instructor: David Jao

Office hours: Wed. & Thurs. 3-4

Administrative

Course materials

Assignments

Lectures

  1. Symmetric vs. public key cryptography. Diffie-Hellman, ElGamal. (http:../../wiki/images/b/be/Lecture01.pdf)
    • Sept. 14
  2. Public key cryptography. Examples and security definitions. (http:../../wiki/images/e/ef/Lecture02.pdf) (updated)
    • Sept. 16, Sept. 28, Sept. 30, Oct. 2
  3. Elementary number theory. Extended Euclidean Algorithm. Order and generators. (http:../../wiki/images/1/11/Lecture03.pdf)
    • Sept. 18, Sept. 21
  4. Quadratic residues, Euler's criterion, Legendre symbols, Quadratic reciprocity. (http:../../wiki/images/e/e0/Lecture04.pdf)
    • Sept. 23, Sept. 25
  5. Jacobi symbols. Jacobi reciprocity. (http:../../wiki/images/c/c8/Lecture05.pdf)
    • Sept. 28
  6. Security and indistinguishability proofs. (http:../../wiki/images/a/a8/Lecture06.pdf)
    • Oct. 5
  7. Why chosen ciphertext security matters. (http:../../wiki/images/5/5f/Lecture07.pdf)
    • Oct. 9
  8. Primality testing. (http:../../wiki/images/b/be/Lecture08.pdf)
    • Oct. 14
  9. Random number generators. (http:../../wiki/images/7/71/Lecture09.pdf)
    • Oct. 16
  10. Zero knowledge proofs. (http:../../wiki/images/4/45/Lecture10.pdf)
    • Oct. 19, Oct. 21
  11. Hash functions and random oracles. (http:../../wiki/images/f/ff/Lecture11.pdf)
    • Oct. 23
  12. Digital signatures. (http:../../wiki/images/5/5d/Lecture12.pdf)
    • Oct. 26, Oct. 28
  13. Chosen ciphertext security. (http:../../wiki/images/0/02/Lecture13.pdf)
    • Oct. 30, Nov. 2, Nov. 4
  14. Integer factorization. (http:../../wiki/images/b/b8/Lecture14.pdf)
    • Nov. 6
  15. Computation of discrete logarithms. (http:../../wiki/images/3/3e/Lecture15.pdf)
    • Nov. 9, Nov. 13
  16. Elliptic curves: introduction and background. (http:../../wiki/images/6/68/Lecture16.pdf)
    • Nov. 11
  17. Implementation of elliptic curves. (http:../../wiki/images/d/df/Lecture17.pdf)
    • Nov. 13
  18. Elliptic curve cryptography. (http:../../wiki/images/2/2f/Lecture18.pdf)
    • Nov. 16
  19. Pairing based cryptography. (http:../../wiki/images/b/b7/Lecture19.pdf)
    • Nov. 18