Jumping right into the second part of your ZK-STARK series, we're focusing on the FRI protocol and its goal of proving the knowledge of a low-degree polynomial. This protocol is a crucial element in the ZK-STARK framework. In the first post on the ZK-STARK series, we:Defined the problem of proving the knowledge of the 12th number in the Lucas sequence.Arithmetized the problem by building a trace and converting it to a polynomial.Extended the domain of the polynomial by adding redundancy ...

Jumping right into the second part of your ZK-STARK series, we're focusing on the FRI protocol and its goal of proving the knowledge of a low-degree polynomial. This protocol is a crucial element in the ZK-STARK framework. In the first post on the ZK-STARK series, we:Defined the problem of proving the knowledge of the 12th number in the Lucas sequence.Arithmetized the problem by building a trace and converting it to a polynomial.Extended the domain of the polynomial by adding redundancy ...

In the first part of the article (refer here), we introduced zero-knowledge proofs and their different types. We started constructing a zk-SNARK for a simple problem by creating an arithmetic circuit, representing it as an R1CS and ultimately converting it into polynomials using QAP. Now that the statement is in polynomial form and ready for cryptography, we'll examine the properties that make polynomials suitable for cryptographic use and investigate some other cryptographic tools avail...

In the first part of the article (refer here), we introduced zero-knowledge proofs and their different types. We started constructing a zk-SNARK for a simple problem by creating an arithmetic circuit, representing it as an R1CS and ultimately converting it into polynomials using QAP. Now that the statement is in polynomial form and ready for cryptography, we'll examine the properties that make polynomials suitable for cryptographic use and investigate some other cryptographic tools avail...

Lately, the DeFi space has emphasized the importance of long-term viability and profitability. This may be a shocking concept to some, but it's natural for protocols to be viewed in a similar way to traditional businesses. Thankfully, the old model of extracting value through inflation is fading away, and projects are now focused on providing actual value to their users. GMX is a great example of a protocol that has embraced this philosophy. It has been available for just over a year but...

Lately, the DeFi space has emphasized the importance of long-term viability and profitability. This may be a shocking concept to some, but it's natural for protocols to be viewed in a similar way to traditional businesses. Thankfully, the old model of extracting value through inflation is fading away, and projects are now focused on providing actual value to their users. GMX is a great example of a protocol that has embraced this philosophy. It has been available for just over a year but...

What is Curve Finance and how does it work? Curve Finance is a decentralized exchange (DEX), that allows users to swap between stablecoins with minimal slippage. The protocol is based on the constant product market maker formula, a major innovation brought by Uniswap. Decentralized exchanges such as Uniswap are great for trading assets with fluctuating price, but do not work well for pairs of stablecoins. The main issue is the price discovery mechanism of the constant product market maker mod...

What is Curve Finance and how does it work? Curve Finance is a decentralized exchange (DEX), that allows users to swap between stablecoins with minimal slippage. The protocol is based on the constant product market maker formula, a major innovation brought by Uniswap. Decentralized exchanges such as Uniswap are great for trading assets with fluctuating price, but do not work well for pairs of stablecoins. The main issue is the price discovery mechanism of the constant product market maker mod...

Liquidity is the lifeblood of DeFi and is crucial for any market to function smoothly. Simply put, liquidity refers to the ability to buy or sell an asset quickly and at a price close to its true value. Liquidity is important for several reasons:It makes trading a better experience, as transactions can be completed almost instantly.It helps to stabilize prices and reduce slippage, or the difference between the price you want to pay for an asset and the price you end up paying.It helps to prev...

Liquidity is the lifeblood of DeFi and is crucial for any market to function smoothly. Simply put, liquidity refers to the ability to buy or sell an asset quickly and at a price close to its true value. Liquidity is important for several reasons:It makes trading a better experience, as transactions can be completed almost instantly.It helps to stabilize prices and reduce slippage, or the difference between the price you want to pay for an asset and the price you end up paying.It helps to prev...

Are you searching for a way to understand zero-knowledge proofs from a technical perspective, but finding existing resources either too shallow or too convoluted? Look no further! This article is for those who, like myself, are not math wizzes, but still want to dive as deep as possible into the topic. So buckle up, and let's start with the basics. Zero-Knowledge Proofs Zero-knowledge proofs (ZKPs) were first brought to light in 1989 with the publication of "The Knowledge Complexity of I...

Are you searching for a way to understand zero-knowledge proofs from a technical perspective, but finding existing resources either too shallow or too convoluted? Look no further! This article is for those who, like myself, are not math wizzes, but still want to dive as deep as possible into the topic. So buckle up, and let's start with the basics. Zero-Knowledge Proofs Zero-knowledge proofs (ZKPs) were first brought to light in 1989 with the publication of "The Knowledge Complexity of I...

In our last piece, we took a deep dive into polynomial commitment schemes, taking a closer look at the renowned KZG10 scheme. Despite many benefits of KZG10, it has a notable shortcoming - the need for a trusted setup. Addressing this issue, we will shift our focus to transparent proofs, also known as zk-STARKs, which eliminate the need for any trusted party. STARKs zk-STARKs (Zero-Knowledge Scalable Transparent ARguments of Knowledge) are a type of cryptographic proof system that allows one ...

In our last piece, we took a deep dive into polynomial commitment schemes, taking a closer look at the renowned KZG10 scheme. Despite many benefits of KZG10, it has a notable shortcoming - the need for a trusted setup. Addressing this issue, we will shift our focus to transparent proofs, also known as zk-STARKs, which eliminate the need for any trusted party. STARKs zk-STARKs (Zero-Knowledge Scalable Transparent ARguments of Knowledge) are a type of cryptographic proof system that allows one ...

Vitalik's recent article, “Don’t Overload Ethereum’s Consensus,” reignited discussions about restaking within the Ethereum community. In this write-up, I aim to shed light on what restaking is and particularly zoom into EigenLayer, the project at the forefront of these conversations. Staking vs. Restaking A majority of you are already familiar with the concept of Ethereum staking. Yet, for clarity's sake: staking was introduced to Ethereum together with its transition to a proof-of-...

Vitalik's recent article, “Don’t Overload Ethereum’s Consensus,” reignited discussions about restaking within the Ethereum community. In this write-up, I aim to shed light on what restaking is and particularly zoom into EigenLayer, the project at the forefront of these conversations. Staking vs. Restaking A majority of you are already familiar with the concept of Ethereum staking. Yet, for clarity's sake: staking was introduced to Ethereum together with its transition to a proof-of-...