Elliptic Curves

Elliptic curves are mathematical shapes defined by specific equations, forming smooth, donut-shaped (toroidal) structures when graphed. They have unique properties allowing us to add points on the curve mathematically, which creates a structured, infinite set of points. This structure is useful in cryptography because the difficulty of reversing these calculations ensures secure digital communication. Essentially, elliptic curves provide a complex, yet manageable mathematical foundation for encrypting data, enabling secure transactions like those in cryptocurrencies and online banking.