EC Cryptography Tutorials - Herong's Tutorial Examples - Version 1.00, by Dr. Herong Yang
Associativity of Elliptic Curve Operations
This section describes the associativity of the addition operation on an elliptic curve. P + (Q + S) = (P + Q) + S is true.
If we want to support multiple addition and subtraction operations sequentially on an elliptic curve, we must verify the "associativity" property of those operations. In other words, is the following statement true or not:
P + (Q + S) = (P + Q) + S
It turns out that the above statement is true. So our addition operation on an elliptic curve is "associative".
You can verify this by following our geometrical steps that defines the addition operation with several example points.
Last update: 2019.
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