But don’t worry, we’ll keep things light and breezy (or as light and breezy as math can be).

So what are these “explicit” addition formulae? Well, they’re a way to add two points on an elliptic curve using some fancy arithmetic. And why would you want to do that? Because it’s essential for the security of many cryptographic protocols!

Now, before we dive into the math, what an elliptic curve is in the first place. It’s basically a curvy line (or “curve”) on a plane that intersects with itself at exactly one point this special point is called the “point at infinity” or just “infinity”.

Okay, got it? Great! So let’s say we have two points on our elliptic curve: P and Q. And we want to add them together using these fancy addition formulae. Here’s how you do it:

1. Calculate the difference between X-coordinates of P and Q (let’s call this value “deltaX”).
2. Calculate the product of Y-coordinate of P, deltaX, and the slope of the line connecting P and Q (let’s call this value “lambda”).
3. Calculate the sum of X-coordinates of P and lambda (let’s call this value “newX”).
4. Calculate the difference between Y-coordinate of P and lambda (let’s call this value “newY”).
5. If newX is equal to infinity, then the result is also infinity. Otherwise, return a point with coordinates (newX, newY).

Woaaw!! That was quite an adventure, wasn’t it? But don’t worry if you didn’t understand everything that’s what we’re here for! If you have any questions or need clarification on anything, feel free to ask. And remember: math is like a rollercoaster ride sometimes it can be scary and confusing, but in the end, it’s always worth it!