EC Cryptography Tutorials - Herong's Tutorial Examples - v1.02, by Dr. Herong Yang
What Is Subgroup in Abelian Group
This section describes Subgroups in a Abelian Group. A subgroup in a Abelian Group is a subset of the Abelian Group that itself is an Abelian Group. The subgroup and its parent group are using the same operation.
What Is Subgroup in Abelian Group? A subgroup in an Abelian Group is a subset of the Abelian Group that itself is an Abelian Group. The subgroup and its parent group are using the same operation.
Group Example 1 - Here is the additive Abelian group of integers: 0, 1, 2, ..., 23 and the addition operation with modular reduction of 24.
Subgroup Example 1.1 - Here is a subgroup in the above group:
Subgroup Example 1.2 - Here is another subgroup in the above group:
Group Example 2 - Here is the multiplicative Abelian group of the Binary Field GF(3^2)/(x^2+1).
Subgroup Example 2.1 - Here is a subgroup in the above group:
The table below defines the addition operation of this subgroup:
+ | 0 1 2 ----------------------- 0 | 0 1 2 1 | 1 2 0 2 | 2 0 1
Subgroup Example 2.2 - Here is another subgroup in the above Abelian Group:
The table below defines the addition operation of this subgroup:
+ | 0 x 2x ----------------------- 0 | 0 x 2x x | x 2x 0 2x | 2x 0 x
Table of Contents
Geometric Introduction to Elliptic Curves
Algebraic Introduction to Elliptic Curves
Abelian Group and Elliptic Curves
Discrete Logarithm Problem (DLP)
►Generators and Cyclic Subgroups
►What Is Subgroup in Abelian Group
What Is Subgroup Generator in Abelian Group
Every Element Is Subgroup Generator
Order of Subgroup and Lagrange Theorem
Element Generated Subgroup Is Cyclic
tinyec - Python Library for ECC
ECDH (Elliptic Curve Diffie-Hellman) Key Exchange
ECDSA (Elliptic Curve Digital Signature Algorithm)