Elliptic Curve

A set of coordinate pairs that satisfy the equation .

⚠️ Prerequisites: Finite fields.

An elliptic curve is defined as the set of all coordinate pairs such that:

In elliptic curve cryptography, we pick and to be elements of a finite field. We refer to this field as the base field.

We then define a group operation which we call “point addition” and usually denote with the ‘’ symbol. Repeated applications of the group operations can be counted like below:

The number ‘’ above is referred to as a scalar. If we are in a cyclic group, then the scalars also define a finite field: we call this field the scalar field.