Abelian Group and Elliptic Curves
This chapter provides an introduction to Abelian Group, which can be expressed in the multiplicative notation or the additive notation. An Abelian Group and be defined on an elliptic curve using the 'rule of chord' operation.
What Is Abelian Group
Niels Henrik Abel and Abelian Group
Multiplicative Notation of Abelian Group
Additive Notation of Abelian Group
Modular Addition of 10 - Abelian Group
Modular Multiplication of 10 - Not Abelian Group
Modular Multiplication of 11 - Abelian Group
Abelian Group on Elliptic Curve
- An Abelian Group is a set of elements and a binary operation
that satisfy 5 conditions.
- An Abelian Group can be expressed in the multiplicative notation.
- All rational numbers with the multiplication operation is an Abelian Group,
and an good example for the multiplicative notation.
- An Abelian Group can be expressed in the additive notation.
- The modular arithmetic addition of any non-negative integer i can
be used to define an Abelian Group, G(i,+).
- The modular arithmetic multiplication of any prime integer p can also
be used to define an Abelian Group, G(p,*).
- An Abelian Group can be defined with all points on an elliptic curve
with the "rule of chord" operation.
Table of Contents
About This Book
Geometric Introduction to Elliptic Curves
Algebraic Introduction to Elliptic Curves
►Abelian Group and Elliptic Curves
Discrete Logarithm Problem (DLP)
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)
EC Cryptography in Java
Standard Elliptic Curves
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