Algebraic Solution for Symmetrical Points

This section provides an algebraic solution for calculating the addition operation of two symmetrical points on an elliptic curve.

Case 1: P and Q are symmetrical points - This case is very easy.

If P and Q are symmetrical points, we know that:
   yQ = - yP
   P + Q = P + (-P) = O (the infinity point or identity element)
   R = O = (∞, ∞)
   xR = 
   yR = 

Table of Contents

 About This Book

 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)

 Finite Fields

 Generators and Cyclic Subgroups

 Reduced Elliptic Curve Groups

 Elliptic Curve Subgroups

 tinyec - Python Library for ECC

 EC (Elliptic Curve) Key Pair

 ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

 ECDSA (Elliptic Curve Digital Signature Algorithm)

 ECES (Elliptic Curve Encryption Scheme)



 Full Version in PDF/EPUB