Elliptic curve cryptography is a modern public-key encryption technique based on mathematical elliptic curves and is well-known for creating smaller, faster, and more efficient cryptographic keys. For example, Bitcoin uses ECC as its asymmetric cryptosystem because of its lightweight nature.
In this introduction to ECC, I want to focus on the high-level ideas that make ECC work. For the purposes of keeping this article easier to digest, I’ll omit implementation details and mathematical proofs, we can save those for another time.
Source: (Very) Basic Intro to Elliptic Curve Cryptography, an article by Lane Wagner.