EC Cryptography Tutorials - Herong's Tutorial Examples - v1.02, by Dr. Herong Yang
Finite Fields
This chapter provides an introduction to Finite Fields. Topics covered include definition of finite fields; examples of finite fields: prime fields GF(p), binary fields GF(2^n) and polynomial fields GF(p^n); field order as the number of elements; field characteristic p is the least positive integer that the scalar multiplication of p and 1 is 0.
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What Is Finite Field
Prime Fields GF(p) - Finite Fields with Modular Arithmetic
Prime Field Example - GF(11)
Binary Fields GF(2^n) on Binary Polynomials
Binary Field Example - GF(2^2) with Modulo x^2+x+1
Binary Field Example - GF(2^3) with Modulo x^3+x+1
Binary Format of Binary Fields GF(2^n)
Binary Format for GF(2^3) with Modulo x^3+x+1
Polynomial Fields GF(p^n) on Prime Polynomials
Polynomial Field Example - GF(3^2) with Modulo x^2+1
Field Order and Field Characteristic
Field Characteristic Is a Prime Number
Field Order Is Prime Power
Takeaways:
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
tinyec - Python Library for ECC
ECDH (Elliptic Curve Diffie-Hellman) Key Exchange
ECDSA (Elliptic Curve Digital Signature Algorithm)