EC Cryptography Tutorials - Herong's Tutorial Examples - v1.02, by Dr. Herong Yang
What Is an Elliptic Curve?
This section describes what is elliptic curve - A set of 2 dimensional points of (x, y) that satisfy the y*y = x*x*x + a*x + b equation with given values of a and b.
What Is an Elliptic Curve? An elliptic curve is the set of 2 dimensional points of (x, y) that satisfy the following mathematical equation with given values of a and b:
y2 = x3 + ax + b
Here are two examples of elliptic curves (source: wikipedia.org):
Here are more examples of elliptic curves (source: wikipedia.org):
Here are some elliptic curves superposed like contour lines (source: cosec.bit.uni-bonn.de):
By the way, the earliest text book discussing elliptic curves is probably the "Arithmetica" by "the father of algebra", Diophantus of Alexandria in the third century.
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)