ABSTRACT
Let F be a finite field and let E be an elliptic curve defined over F. Since there are only finitely many pairs (x, y) with x, y ∈ F, the group E(F) is finite. Various properties of this group, for example, its order, turn out to be important in many contexts. In this chapter, we present the basic theory of elliptic curves over finite fields. Not only are the results interesting in their own right, but also they are the starting points for the cryptographic applications discussed in Chapter 6.
