What the hell is an elliptic curve?

Have you ever been browsing the web and come across a term that made you go, "huh?" Well, if you're even slightly cryptographcally inclined, you might have stumbled upon the term elliptic curve and thought to yourself, "What the hell?" Don't worry, you're not alone in feeling a bit lost. An elliptic curve is a type of mathematical function that has some pretty cool properties. It's defined by a specific equation, usually in the form of y 2 = x 3 + a x + b y^2 = x^3 + ax + b y2=x3+ax+b, where a a a and b b b are constants. The graph of this equation looks like a smooth, looping curve, which is where the name "elliptic" comes from. These curves have a unique feature: they can be used to create a group of points that can be added together in a unique way to form new points. This is what makes them so useful in cryptography. (The graphs below are interactive, you can zoom, pan, etc.) SHORT WEIERSTRASS FORM: y² = x³ - x + 1 f: R → R Elliptic curves are used in various cryptographic algo ... Read full article.