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Educational Hub
Elliptic Curve Visualizer (Secp256k1)
Bitcoin uses the Secp256k1 elliptic curve defined by the equation y² = x³ + 7. Visualize its continuous shape and mathematically calculate the coordinates of the Public Key over the finite Prime Field.
1
Geometric Shape over Real Numbers
Representation of y² = x³ + 7. Geometrically, adding a point to itself (P + P) implies drawing a tangent, finding the intersection, and reflecting it on the X-axis to get 2P. Bitcoin does this trillions of times over a finite Prime Field.
2
Scalar Multiplication (Prime Field)
Multiply the Generator Point G by your scalar (Private Key). The algorithm instantly calculates the X, Y coordinates of your Public Key by bouncing across the curve.
X
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Y
Waiting for calculation...