Week | Topic | Course Work |
Jan. 9 |
Introduction to Finite Fields (overview, structure, construction, and automorphisms) |
  |
Jan. 16 |
Introduction to Elliptic Curves (definitions, group structure, affine and
projective coordinates) |
Jan. 20
Assignment 1 set
|
Jan. 23 |
Alternative Models (characteristic 2 and 3, Legendre model, quartic equation |
  |
Jan. 30 |
Isomorphisms and Isogenies (elliptic function fields, isogenies) |
  |
Feb. 6 |
Endomorsphism Rings |
Feb. 10 Assignment 1 due (hard copy in class); Assignment 2 set
|
Feb. 13 |
Torsion Points and the Weil Pairing |
  |
Feb. 20 |
Reading week |
  |
Feb. 27 |
Elliptic Curves over Finite Fields (group order, anomalous curves, supersingular curves) |
March 2 Proposal due (hard copy in class) |
March 5 |
Elliptic Curve Cryptography (ECDSA, ECIES, ECMQV, need for public key verification) |
March 9 Assignment 2 due (hard copy in class); Assignment 3 set
|
March 12 |
Security of Elliptic Curve Cryptography (generic algorithms for the ECDLP, weak curves) |
  |
March 19 |
Efficient Implementation (finite field arithmetic, point addition and doubling, point multiplication) |
  |
March 26 |
Additional Topics (Koblitz curves, pairing-based cryptography) |
  |
April 2 |
Divisors and the Weil Pairing |
April 6 Assignment 3 due (hard copy in class) |
April 9 |
Student presentations |
April 13 Research project due (hard copy in class) |