Elliptic Curve Cryptography 2D: Finite-Field Point Addition & ECDH

This 2D companion to the 3D Elliptic Curve simulator moves the same group law from the continuous real numbers into an actual finite field F_p, which is what every real ECC deployment uses. Pick a curve y² = x³ + ax + b (mod p), and the lab enumerates every point on it by brute-force search, finds a generator of maximal order, and lets you add or double points using the real modular-inverse formulas — visualised as a wraparound chord that breaks and reappears on the opposite edge of the field each time the line's y-value wraps past 0 or p. Switch to scalar mode to watch k·P built one bit at a time by the double-and-add algorithm, the same ladder used inside every production ECC implementation, or switch to ECDH mode to run a complete Diffie-Hellman key exchange over the curve: Alice and Bob each pick a private scalar, exchange public points, and independently multiply the other's public point by their own private key to land on the identical shared secret — computed live with BigInt, not staged.