**EC Cryptography Tutorials - Herong's Tutorial Examples** - v1.00, by Dr. Herong Yang

Subtraction Operation on an Elliptic Curve

This section describes the Subtraction operation on an elliptic curve. If the resulting point of the subtraction operation of point Q from P, then P - R = P + (-Q)..

With the introduction of the negation operation, we can easily define the subtraction operation on an elliptic curve as the following.

If we use the minus sign "-" as the negation operator, then the resulting point R of the subtraction operation of a point Q from P on an elliptic curve can be expressed as the following:

R = P - Q = P + (-P), where (-Q) is the negation operation of Q

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)