Elliptic Curve

A mathematical structure defined by an equation of the form y² = x³ + ax + b over a finite field, used in public-key cryptography because discrete logarithms on the curve are computationally hard. Bitcoin and Ethereum both use the secp256k1 curve; a 256-bit private key maps to a unique public key, but deriving the private key from the public key is infeasible with current hardware.