This can continue, using the initial point and the newly acquired point as necessary: You then go to the x-axis opposite (up or down) to find a third point, point C. In the brilliant animation above (all credit goes to the original author, Nick Sullivan), the author explained that the heart of EC Crypto is that if you take any two points on the curve, A and B, and draw a line from A to B, and then continue the line you end intersecting one, and only one, other point on the curve. The crux of the article is in page two, namely, when it discussed the "dot" operation: It was able to explain Elliptic Curves to me in a way that didn't require a math degree to understand. I read a brilliant, three part article on Elliptic Curve cryptography ( one, two, three).
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