origin :
https://steemit.com/blockchain/@lanecwagner/very-basic-elliptic-curve-cryptography
This is probably why most of you are here. This is what makes ECC special and different from RSA. The trapdoor function is similar to a mathematical game of pool. We start with a certain point on the curve. We use a function (called the dot function) to find a new point. We keep repeating the dot function to hop around the curve until we finally end up at our last point. Lets walk through the algorithm.
Starting at A:
A dot B = -C (Draw a line from A to B and it intersects at -C)
Reflect across the X axis from -C to C
A dot C = -D (Draw a line from A to C and it intersects -D)
Reflect across the X axis from -D to D
A dot D = -E (Draw a line from A to D and it intersects -E)
Reflect across the X axis from -E to E
This is a great trapdoor function because if you know where the starting point (A) is and how many hops are required to get to the ending point (E), it is very easy to find the ending point.
Known Point : Starting Point A
Public Key: Ending Point E
Private Key: Number of hops from A to E
Answer: No. The second point (we will call it -R below) is actually the result of P dot P (let’s assume the first point is called P)
P dot P= -R
So what is P dot P? It is actually just the tangent line of P. See the graphic below:
