Visualise point addition and scalar multiplication on an elliptic curve y² = x³ + ax + b. See how multiplying a generator point by a large scalar creates a keypair — and why reversing it is computationally infeasible.
Point addition on an elliptic curve: a line through two points P and Q intersects the curve at a third point, which is reflected to give P+Q. Scalar multiplication k·P repeats this operation k times. The discrete log problem on elliptic curves is believed to require exponential time.
Click two points on the curve to add them. Use scalar mode to multiply the generator point by increasing k. Watch the resulting point jump unpredictably around the curve — illustrating the one-way trapdoor.
Elliptic curve cryptography achieves the same security as RSA-3072 with only 256-bit keys — a 12× reduction in key size. Bitcoin's secp256k1 curve processes millions of transactions daily using this exact mathematics.