**EC Cryptography Tutorials - Herong's Tutorial Examples** - v1.03, by Herong Yang

Algebraic Solution for the Infinity Point

This section provides an algebraic solution for calculating the addition operation of two points on an elliptic curve with one of them is the infinity point.

Case 2: P or Q is the infinity point - This case is also very easy.

If: P = O = (∞, ∞) We know that: P + Q = O + Q = Q So: R = Q x_{R}= x_{Q}y_{R}= y_{Q}If: Q = O = (∞, ∞) We know that: P + Q = P + O = P So: R = P x_{R}= x_{P}y_{R}= y_{P}

Table of Contents

Geometric Introduction to Elliptic Curves

►Algebraic Introduction to Elliptic Curves

Algebraic Description of Elliptic Curve Addition

Algebraic Solution for Symmetrical Points

►Algebraic Solution for the Infinity Point

Algebraic Solution for Point Doubling

Algebraic Solution for Distinct Points

Elliptic Curves with Singularities

Elliptic Curve Point Addition Example

Elliptic Curve Point Doubling Example

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)