OBSERVATION CHAMBER / ACTIVE
Elliptic Curve Group Law
Place two points on an elliptic curve, trace the chord or tangent, and compare exact addition over rational presets and small finite fields.
geometry
Operational
02
WATCH THE LAW
Curve and construction
PQR = P + Qthird intersection
03
READ THE RESULT
Group-law result
NOT COMPUTED
P + Q = —
Choose two points and trace their sum.
- operation
- —
- slope
- —
- curve
- smooth
- order of P
- —
SYSTEM NOTE
For E: y²=x³+ax+b with 4a³+27b²≠0, use λ=(yQ−yP)/(xQ−xP) for a chord or λ=(3xP²+a)/(2yP) for a tangent. Then xR=λ²−xP−xQ and yR=λ(xP−xR)−yP. The identity is O, P+O=P, and P+(−P)=O. Over Fp, division means multiplication by a modular inverse.
OBSERVATION POLICY
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