An elliptic curve is a type of smooth, non-singular curve defined by a specific mathematical equation, typically in the form y^2 = x^3 + ax + b. These curves have interesting properties and are used in various areas of mathematics, including number theory and algebraic geometry. Elliptic curves are particularly important in cryptography, where they provide a framework for secure communication. The security of systems like Elliptic Curve Cryptography (ECC) relies on the difficulty of solving certain problems related to these curves, making them efficient for encrypting data and ensuring secure transactions.