Implementations of SEA Algorithm Counting the Orders of Elliptic Curve Groups over Binary Fields

The best suggested way to find secure elliptic curves is point-counting. So far Schoof-Elkies-Atkin algorithm (SEA algorithm) is the most efficient point-counting algorithm for elliptic curves over prime fields. Lercier proposed an algorithm to compute isogenies in GF(2^n) such that SEA algorithm can be used for binary case. In this thesis we will follow Lericier''s approach to implement SEA algorithm computing the order of an elliptic curve over binary fields.