| Week | Topic | Course Work |
| 11/01 |
Introduction to Finite Fields (overview, structure, construction, and automorphisms) |
|
| 18/01 |
Introduction to Elliptic Curves (definitions, group structure, affine and
projective coordinates) |
21/01
Assignment 1 set
|
| 25/01 |
Alternative Models (characteristic 2 and 3, Legendre model, quartic equation |
|
| 01/02 |
Isomorphisms and Isogenies (elliptic function fields, isogenies) |
|
| 08/02 |
Endomorsphism Rings |
12/02 Assignment 1 due; Assignment 2 set
|
| 15/02 |
Reading week |
|
| 22/02 |
Torsion Points and the Weil Pairing |
|
| 01/3 |
Elliptic Curves over Finite Fields (group order, anomalous curves, supersingular curves) |
05/03 Proposal due (hard copy by 16:00 in my office) |
| 08/03 |
Elliptic Curve Cryptography (ECDSA, ECIES, ECMQV, need for public key verification) |
12/03 Assignment 2 due; Assignment 3 set |
| 15/03 |
Security of Elliptic Curve Cryptography (generic algorithms for the ECDLP, weak curves) |
|
| 22/03 |
Efficient Implementation (finite field arithmetic, point addition and doubling, point multiplication) |
|
| 29/03 |
Additional Topics (Koblitz curves, pairing-based cryptography) |
02/09 Assignment 3 due |
| 05/04 |
Divisors and the Weil Pairing |
|
| 12/04 |
Student presentations |
16/04 Research project due (hard copy by 16:00 in my office) |