| Week | Topic | Course Work |
| Jan. 8 |
Introduction to Finite Fields (overview, structure, construction, and automorphisms) |
|
| Jan. 13 |
Introduction to Elliptic Curves (definitions, group structure, affine and
projective coordinates) |
Jan. 17
Assignment 1 set
|
| Jan. 20 |
Alternative Models (characteristic 2 and 3, Legendre model, quartic equation |
|
| Jan. 27 |
Isomorphisms and Isogenies (elliptic function fields, isogenies) |
|
| Feb. 3 |
Endomorsphism Rings |
Feb. 7 Assignment 1 due (hard copy in class); Assignment 2 set
|
| Feb. 10 |
Torsion Points and the Weil Pairing |
|
| Feb. 17 |
Reading week |
|
| Feb. 24 |
Elliptic Curves over Finite Fields (group order, anomalous curves, supersingular curves) |
Feb 28 Proposal due (hard copy in class) |
| March 3 |
Elliptic Curve Cryptography (ECDSA, ECIES, ECMQV, need for public key verification) |
March 9 Assignment 2 due (hard copy in class); Assignment 3 set
|
| March 10 |
Security of Elliptic Curve Cryptography (generic algorithms for the ECDLP, weak curves) |
|
| March 17 |
Efficient Implementation (finite field arithmetic, point addition and doubling, point multiplication) |
|
| March 24 |
Additional Topics (Koblitz curves, pairing-based cryptography) |
|
| March 31 |
Divisors and the Weil Pairing |
April 4 Assignment 3 due (hard copy in class) |
| April 7 |
Student presentations |
April 11 Research project due (hard copy in class) |