EC Cryptography Tutorials - Herong's Tutorial Examples - v1.02, by Dr. Herong Yang
Abelian Group on Elliptic Curve
This section demonstrates that an Abelian Group can be defined with all points on an elliptic curve with the 'rule of chord' operation.
The addition operation we have defined earlier on an elliptic curve actually helps to create an Abelian Group on the curve:
You can verify that all 5 Abelian Group conditions are satisfied. For example:
P + Q = R The "closure" condition P + Q = Q + P The "commutativity" condition (P + Q) + S = P + (Q + S) The "associativity" condition P + ∞ = P The "identity" condition P + (-P) = ∞ The "symmetry" condition
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