An elliptic curve is the set of points satisfying y² = x³ + ax + b. Its points can be added to each other, and repeating that addition is easy to do but practically impossible to undo. That one-way step protects HTTPS, Bitcoin, Signal and SSH.
To add P and Q: draw the line through them, find where it hits the curve a third time, then flip that point over the x-axis. The flipped point is P + Q. To double a point (P + P), use the tangent line at P. Click on the curve to move P and Q.
Cryptography uses whole numbers modulo a prime p instead of real numbers. The smooth curve becomes a scatter of dots, but the addition formulas stay exactly the same, just done mod p. Click any dot to make it the base point G, then slide k to watch k·G jump around.
Notice how G, 2G, 3G, … land in no visible pattern. Knowing the result k·G gives no clue about k. That is the whole security idea.
Alice and Bob agree on the curve and G in public. Each picks a secret number, multiplies G by it, and sends the result. Each then multiplies the other's point by their own secret, and both land on the same point. Eve sees everything sent but not the secrets.
Adding G to itself α times would be slow for huge α. Instead, write α in binary and keep doubling G, adding in the doublings where the bit is 1. Even a 256-bit secret takes only about 256 doublings.
Eve knows the curve, G, A and B. To find the shared secret she must recover α from A = α·G. This is the elliptic-curve discrete logarithm problem. On this toy curve she can simply try every k.