**EC Cryptography Tutorials - Herong's Tutorial Examples** - v1.02, by Dr. Herong Yang

Standard Elliptic Curves

This chapter provides tutorial notes on standard elliptic curves. Topics covered include a list of standard curves; domain parameters of some commonly used standard curves; generating and views private-public key pairs associated domain parameters.

What Are Standard Elliptic Curves

"openssl ecparam -list_curves" - Curves Supported by OpenSSL

"secp256r1" - For 256-Bit ECC Keys

"secp256k1" - For 256-Bit ECC Keys

"sect283r1" - For 256-Bit ECC Keys

Takeaways:

- "openssl ecparam -list_curves" lists most standard elliptic curves.
- Most popular standard elliptic curves are selected and recommended by SECG (Standards for Efficient Cryptography Group).

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)