Elliptic curves are useful because of something called point addition. Point addition is where we can do an operation on two of the points on the curve and get a third point, also on the curve. This is called addition because the operation has a lot of the intu‐ itions we associate with the mathematical operation of addition. For example, point addition is commutative. That is, adding point A to point B is the same as adding point B to point A.
One of the properties that we are going to use is that point addition is not easily pre‐ dictable. We can calculate point addition easily enough with a formula, but intuitively, the result of point addition can be almost anywhere given two points on the curve. Going back to Figure 2-14, A + B is to the right of both points, A + C would be some‐ where between A and C on the x-axis, and B + C would be to the left of both points. In mathematics parlance, point addition is nonlinear.
a. Points X1 != X2