If you don’t know what ECC is, well…you should probably go back to school or something. But for those of us who do know what it is, let me explain why we care about Edwards curves specifically.

First off, elliptic curve cryptography in general. It’s a fancy way of saying that instead of using traditional RSA encryption (which involves factoring large numbers), we can use math to create secure keys and encrypt data. And the beauty of ECC is that it uses much smaller key sizes than RSA, which means faster processing times and less storage space required for those ***** digital certificates.

But here’s where things get interesting: instead of using traditional elliptic curves (which are defined by a cubic equation), we can use Edwards curves (defined by a quadratic equation). And the reason why this is so awesome is because it makes our calculations faster and more efficient, which means better performance overall.

So what exactly does an Edwards curve look like? Well, let’s take a look at one of the most popular examples: Curve25519 (which has a 255-bit key size). This particular curve is defined by the following equation: y^2 = x^3 + 486662x^2 + x

Now, if you’re not familiar with math notation, that might look like gibberish to you. But trust me when I say that it’s actually pretty simple once you break it down. Essentially, we’re just saying that for any given point (x, y) on this curve, the value of y squared is equal to x cubed plus 486662 times x squared plus x.

And here’s where things get really interesting: instead of using traditional addition and multiplication operations to calculate points on an Edwards curve, we can use a technique called “doubling” (which involves multiplying by -1) and “addition” (which involves adding two points together). And the reason why this is so awesome is because it makes our calculations faster and more efficient than traditional methods.

It’s a fancy way of saying that we can use math to create secure keys and encrypt data, but with smaller key sizes and faster processing times thanks to the magic of quadratic equations. And if you ask me, that’s pretty ***** cool.

Now, if you’ll excuse me, I have some digital certificates to sign and some data to encrypt. But before I go, let me leave you with this final thought: math is awesome.