Mastering Blockchain - Second Edition

Point doubling

The other group operation on elliptic curves is called point doubling. This is a process where P is added to itself. In this method, a tangent line is drawn through the curve, as shown in the following graph. The second point is obtained, which is at the intersection of the tangent line drawn and the curve.

This point is then mirrored to yield the result, which is shown as 2P = P + P:

Graph representing point doubling over real numbers

In the case of point doubling, the equation becomes:

Here, S is the slope of tangent (tangent ...