Mathematics

Time for our first basic mathematical concepts!

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

To close things off, we look at homomorphic encryption again, this time on rings!

Time to build some cryptographic methods out of rings and their associated hard problems

Now that we know about rings, we need a hard problem to work out some cryptography from them — enter Ring Learning With Errors!

Before moving onto the latest frontier of cryptography — post-quantum cryptography — , we need to lay down some more groundwork!

Following from SNARKs, we now explore another type of knowledge proofs tailored for scalability

Let’s get practical, and build some arithmetic circuits!

This second round of zero knowledge proofs will take us on a journey to understand a more general framework. Hang tight!

Before moving on into more complex zero knowledge proofs, we need to introduce a new model: arithmetic circuits!

We take a leap into the world of zero-knowledge proofs by exploring one of the many ZKP protocols out there: Bulletproofs

An expansion upon the ideas behind simpler commitment schemes, providing important tools for more complex constructions down the road

Following our presentation of pairings, we look at a couple more applications enabled by this new tool

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

Combining polynomials and digital signatures brings forth a cool new functionality, in the form of Threshold Signatures!

Polynomials play an important role in many cryptographic applications. This article is dedicated to giving a brief intro to the topic

A deeper dive into core concepts of groups, and a fascinating application: homomorphic encryption

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

A short explanation on how RSA works

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

A very gentle intro into the world of cryptography