I'm trying to understand the graphical basis that underlies the discreet logarithmic Elliptic Curve Digital Signature Algorithm (ECDSA) introduced in Chapter 4 of "Mastering Bitcoin" by Andreas Antonopolous: https://github.com/aantonop/bitcoinbook/blob/develop/ch04.asciidoc
Andreas says a point in an elliptic curves can be added to itself by drawing a tangent, finding the intersection, then reflecting the new point on the x-axis. This makes no sense to me, but for now I'll just blindly believe. Then K = k * G, where k is the private key, G is a constant "Generator Point" and K is the public key.
Then he shows the attached figure which graphically shows how to get from G to 8G.
- Is "8" the private key in this example?
- Given K and G, it doesn't seem like this function would be irreversible. Am I missing something or does it only become irreversible in the discrete logarithmic equivalent.