Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security.
An elliptic curve is a plane curve over a finite field (rather than the real numbers) which consists of the points satisfying the equation:
y² = x³ + ax + b