Elliptic Curves

After stocking up with hashes, now's time for another big protagonist of this ZK story!

To wrap up the series, we take a look at a few practical aspects, and present some of the most studied elliptic curves out there.

A wrap-up on pairings, with some discussions around algorithms, types, and other nuances.

With torsion groups at hand, we can now explore the formal definition of pairings.

Setting up the bases to later define pairings, this article explores torsion groups!

An examination of some of the behind-the-scenes action that enables ECC, accompanied with brief look at a long-standing problem in math.

This time we cover divisors, and analyze how they play into the world of elliptic curves, revealing some new secrets.

Let’s talk about functions on elliptic curves, and their crazy properties.

Time to focus on the most relevant aspect about elliptic curves in cryptography: their group structure.

We now move from our familiar real number setting, to the realm of finite fields, where elliptic curves really shine.

A (kinda) gentle intro to elliptic curves

A brief introduction to pairings, an important tool in modern cryptography

A quick look at some slightly more elaborate signature schemes than usual

Building upon our previous knowledge of elliptic curves, we explore how to encrypt and sign information

An introductory dive into the world of elliptic curves, forming the basis for understanding useful cryptographic mechanisms