Let $E(\mathbb{R} )$ be the elliptic curve group over $\mathbb{R}$ given by $ y^2=x^3+1$ and $P = (2,3) $.
Calculate 2P, 3P, 4P.
I know how to add elliptic curve points, wether they are the same or not, however, I believe their is a system for using a scalar, n, for calculating $nP$.
I have heard about the double and add method however I can't get my head around it.
Suppose you want to calculate $100P$.
With the double and add method, instead of computing $$2P=P+P \\3P=2P+P \\4P=3P+P\\5P=4P+P\\6P=5P+P \\ \vdots \\ 99P = 98P+P \\ 100P = 99P + P$$ you just compute $$2P=P+P\\4P=2P+2P\\8P=4P+4P\\ 16P=8P+8P \\ 32P=16P+16P \\ 64P=32P+32P \\ 100P=64P+32P+4P.$$