**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.

Table of Contents

►Geometric Introduction to Elliptic Curves

Elliptic Curve Geometric Properties

Addition Operation on an Elliptic Curve

Prove of Elliptic Curve Addition Operation

Same Point Addition on an Elliptic Curve

Infinity Point on an Elliptic Curve

Negation Operation on an Elliptic Curve

Subtraction Operation on an Elliptic Curve

Identity Element on an Elliptic Curve

Commutativity of Elliptic Curve Operations

►Associativity of Elliptic Curve Operations

Elliptic Curve Operation Summary

Algebraic Introduction to Elliptic Curves

Abelian Group and Elliptic Curves

Discrete Logarithm Problem (DLP)

Generators and Cyclic Subgroups

tinyec - Python Library for ECC

ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

ECDSA (Elliptic Curve Digital Signature Algorithm)