Frank Mangone

Our journey now leads us into another big player in the Blockchain space: Solana

Before we jump into other Blockchain solutions, let’s explore the ecosystem built around Ethereum

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

A few last comments on important architectural aspects of Ethereum, rounding up the section on this Blockchain!

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

A short explainer on how quantum computers work, what they can do, and what to expect from them in the near future

Exploring the consensus mechanism behind Ethereum: Proof of Stake

Let’s talk about functions on elliptic curves.

A more functional approach to Smart Contracts, exploring Solidity in further detail

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 peek into the architecture that makes Smart Contracts possible in Ethereum

Time to look at the machinery behind Ethereum’s storage!

Time to move on to the second big milestone in Blockchain’s history: Ethereum

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

With this fourth article, we finish our brief pass through Bitcoin by looking at a couple missing key points.

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

Let’s shift our focus to how a decentralized system can agree on a single truth: through consensus.

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

Let's focus on the lifeblood of Blockchains early: Transactions!

We embark on a new journey, where we explore the amazing technology of Blockchains

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

Short summary of some important aspect of security in 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 gentle introduction to some very useful schemes: key exchange, commitment schemes, zero-knowledge proofs, verifiable random functions

A short explanation on how RSA works

Hashing functions are an essential cryptographic primitive. Join me in a deep dive into what they are, and what they are used for!

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