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Point Addition
Visualizing the elliptic curve group operation
Point P (click to place)
Not set
Point Q (click to place)
Not set
Result P + Q = R
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Addition Formula
λ = (y₂ - y₁) / (x₂ - x₁)
x₃ = λ² - x₁ - x₂
y₃ = λ(x₁ - x₃) - y₁
Curve: y² = x³ - x + 1
To add P and Q:
1. Draw line through P and Q
2. Find third intersection R'
3. Reflect R' over x-axis to get R
Reset Points
Animate Addition
Click on the curve to place points P and Q. The visualization will show the geometric construction of their sum.