Question

For cryptography, the variables and coefficients are usually elements of

Answer 1

An elliptic curve is defined by an equation in two variables, with coefficients. For cryptography, the variables and coefficients are restricted to elements in a finite field.

Answer 2

Finite is the answer.

Crptography:

Fp Prime Field Elliptic Curves

F2 m Binary Field Elliptic Curves

Elliptic Curve equation variables and coefficients are all limited to these finite fields. These sections use an affine coordinate system, which is a normal coordinate system in which each point is represented by a vector (X,Y).