How is point addition on an elliptic curve defined geometrically?
Conditions
- A and B are points on the elliptic curve.
- The line through A and B intersects the curve at a third point.
- The curve is symmetric about the x-axis.
Reasoning, step by step
- Draw the straight line through points A and B.
- Identify the third intersection point of that line with the curve.
- Reflect that third intersection point across the x-axis.
- Label the reflected point as C, so .
Example
The video shows an animation where a line is drawn through points A and B, intersects the curve at a third point, and is then reflected across the x-axis to point C.
Common misconceptions
- Adding the x and y coordinates of A and B directly.
- Forgetting to reflect the third intersection point across the x-axis.
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