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, pairingbased 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) 