Elliptic Curves introduction

A beginner-friendly walkthrough of elliptic curve cryptography fundamentals. Using a small toy curve (y² = x³ + 2x + 2 mod 17), it explains how points on a curve are defined over a finite field, how scalar multiplication works, and how the generator point G produces a cyclic group. The post then demonstrates Diffie–Hellman key exchange step by step with concrete numbers, showing how Alice and Bob derive the same shared secret without ever transmitting their private keys. The security foundation — the Elliptic Curve Discrete Logarithm Problem (ECDLP) — is explained intuitively as the one-way difficulty of reversing scalar multiplication.