1. (Difficult): What is a component of a cubic polynomial? And what does the top and bottom of the y-axis mean? Also, an example of change of variables would be good.
Lastly, what's the point of the Law of Addition in regards to elliptic curves? And the "point" infinity from which we define negatives and subtraction is still confusing. I'M NOT GETTING THE GEOMETRICAL MEANING BEHIND THE LAW OF ADDITION, INFINITY, SUBTRACTION AND ANYTHING ASSOCIATED WITH ELLIPTIC CURVES.
2. (Reflection): The computational summary at the end is nice. I would still like to understand this subject thoroughly by knowing why the formulas work by understanding the real geometrical meaning behind elliptic curves.
Furthermore, how is this going to help with cryptography? Is it going to be for more secret splitting or something like that where 3 people have parts of the secret and it takes two to get the secret (two points determine a third point and the elliptic curve)?
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