Generators and Cyclic Subgroups

This chapter provides introduction on generating subgroups from elements in finite Abelian groups; definitions and examples of subgroup generators, subgroup order, cyclic subgroups, Lagrange-Theorem.

What Is Subgroup in Abelian Group

What Is Subgroup Generator in Abelian Group

What Is Order of Element

Every Element Is Subgroup Generator

Order of Subgroup and Lagrange Theorem

What Is Cyclic Group

Element Generated Subgroup Is Cyclic

Conclusion:

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)

 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)

 Terminology

 References

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