**EC Cryptography Tutorials - Herong's Tutorial Examples** - Version 1.00, by Dr. Herong Yang

Negation Operation on an Elliptic Curve

This section describes the Negation operation on an elliptic curve. If the resulting point the negation operation of an given point P is R, then P + R is the infinity point.

With the introduction of the infinity point, we can now define another operation on an elliptic curve, the negation operation, which is a unary operation.

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

R = -P, if P + R is the infinity point.

If we use letter O to represent the infinity point, the above expression can be shortened as the following:

R = -P, if P + R = O

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)