Point Addition

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.

*nonlinear*. This is rings the bell that hashing supposedly one-way process.

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

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