Reduced Elliptic Curve Groups

This chapter provides notes and tutorials on reduced elliptic curve groups. Topics include elliptic curve on in integer space; elliptic curves and the addition operation reduced by modular arithmetic; elliptic curve groups and examples.

Converting Elliptic Curve Groups

Elliptic Curves in Integer Space

Python Program for Integer Elliptic Curves

Elliptic Curves Reduced by Modular Arithmetic

Python Program for Reduced Elliptic Curves

Point Pattern of Reduced Elliptic Curves

Integer Points of First Region as Element Set

Reduced Point Additive Operation

Modular Arithmetic Reduction on Rational Numbers

Reduced Point Additive Operation Improved

What Is Reduced Elliptic Curve Group

Reduced Elliptic Curve Group - E23(1,4)

Reduced Elliptic Curve Group - E97(-1,1)

Reduced Elliptic Curve Group - E127(-1,3)

Reduced Elliptic Curve Group - E1931(443,1045)

What Is Hasse's Theorem

Finite Elliptic Curve Group, Eq(a,b), q = p^n

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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