Elliptic Curve Cryptography: Point Operations & ECDH

Elliptic-curve cryptography secures most of today's encrypted web traffic, signatures and key exchanges, and its entire security rests on one geometric operation: adding two points on a curve. This simulation splits that idea into two linked views. The first plots a real-number curve y² = x³ + ax + b and lets you drag two points along it to watch the secant-line construction that defines point addition and doubling — the group law ECC is built on. The second switches to a tiny finite field, where the same curve's points can be enumerated on a grid, and animates the double-and-add scalar multiplication that two parties use to compute matching public keys and a shared secret in an elliptic-curve Diffie-Hellman (ECDH) exchange — without ever transmitting their private keys.