An elliptic curve is a type of smooth, continuous curve defined by a specific mathematical equation, typically in the form y^2 = x^3 + ax + b. These curves have unique properties that make them useful in various fields, including number theory and cryptography. The points on an elliptic curve can be added together using a defined geometric process, which leads to interesting algebraic structures. In cryptography, elliptic curves are used to create secure encryption methods, such as Elliptic Curve Cryptography (ECC). This approach allows for smaller keys compared to traditional methods, providing the same level of security with increased efficiency. As a result, elliptic curves play a significant role in securing digital communications and transactions.