Point doubling

Point doubling is a similar operation to point addition, with the exception that point Q is moved to the same location as point P (P = Q):

The following steps are performed on the elliptic curve as shown in Figure 2.8 to compute point doubling:

1. Draw a tangent (since there is only one point) to the curve at point P
2. This line will intersect the curve at point R1
3. A reflection of point R1 about the x axis gives point R, and this is point doubling or a multiple of R (2R)

Point doubling is the concept used in ECC to construct the public key from the private key. The following section explains in depth how point doubling is used in the generation of the public key.