Elliptic Curve (ECC) Visualizer
See an elliptic curve over a prime field and the point-addition group law that secures crypto keys.
🔒 100% in your browser — nothing is uploaded
A toy elliptic curve y² = x³ + ax + b over a prime field. The same group law secures real keys — only the prime is astronomically larger.
How it works
Pick a small curve y² = x³ + ax + b over a prime field and see every point plotted, then choose two points P and Q to watch the group law produce P + Q. This is the exact arithmetic behind ECDSA and Bitcoin/Ethereum keys (secp256k1) — only the prime there is a 256-bit number instead of a handful, so the points can’t be plotted but the rules are identical.
Educational toy curves only — far too small for any real security.
Frequently asked questions
What am I looking at?
Every (x, y) pair that satisfies the curve equation over the chosen prime field. Real elliptic-curve crypto uses the same structure over an enormous prime.
How does point addition work?
Draw a line through P and Q; it meets the curve at a third point, which is reflected to give P + Q. Over a finite field the same is computed with modular arithmetic.
What is the point at infinity?
The identity element of the group — it acts like zero, so P + (−P) = ∞.