sorry: for nerds only
The eliptic curve signature
An eliptic curve is drawn by the formula y² = x³ + ax + b (so no magic at all)
And a Point P on the curve is described by two coordinates (p1, p2)
And based on this curve we can now easily compute operations like an addition.
We know that P+Q+R= 0 (because they are all on one line)
So P+Q= -R (because based on P+Q+R = 0 you get P+Q only by subtracting R)
Of course, you can also do multiplication
Scalar multiplication
First let´s do a check:
P + Q + Q = 0 (right? Because they are all on one line)
So, Q + Q or 2Q is -P (2Q= -P; because you need to subtract P from P + 2Q = 0)
Now you have understood the mathematical operation behind ECDSA (or maybe not, because your Brain has a conditioned fear of math, even if it is simple. Thank you school 🙂 ). Of course Bitcoin uses a special algorithm. Just like a cooking-recipe only based on the principles above.
