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Maksym
Maksym

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Apr 25, 2019

Why and How zk-SNARK Works 8: Zero-Knowledge Computation

This is a series of articles. Part 7,​ ​ PDF version Zero-Knowledge Proof of Computation Since the introduction of the general-purpose computation protocol (Proof of Operation section) we had to let go of the zero-knowledge property, to make the transition simpler. Until this point, we have constructed a verifiable computation protocol. Previously to make…

Privacy

8 min read

Why and How zk-SNARK Works 8: Zero-Knowledge Computation
Why and How zk-SNARK Works 8: Zero-Knowledge Computation
Privacy

8 min read


Apr 23, 2019

Why and How zk-SNARK Works 7: Constraints and Public Inputs

This is a series of articles. Part 6,​ ​ PDF version Constraints Our analysis has been primarily focusing on the notion of operation. However, the protocol is not actually “computing” but rather is checking that the output value is the correct result of an operation for the operand’s values. That is…

Mathematics

5 min read

Why and How zk-SNARK Works 7: Constraints and Public Inputs
Why and How zk-SNARK Works 7: Constraints and Public Inputs
Mathematics

5 min read


Apr 19, 2019

Why and How zk-SNARK Works 6: Verifiable Computation Protocol

This is a series of articles. Part 5,​ ​ PDF version We went through many important modifications of the knowledge of polynomial protocol to make it general-purpose, so let us see how it is defined now. …

Mathematics

8 min read

Why and How zk-SNARK Works 6: Verifiable Computation Protocol
Why and How zk-SNARK Works 6: Verifiable Computation Protocol
Mathematics

8 min read


Apr 16, 2019

Why and How zk-SNARK Works 5: Variable Polynomials

This is a series of articles. Part 4, ​ ​PDF version With the multi-operation polynomials approach introduced in part 4, we can prove many operations at once (e.g., millions and more), but there is a critical downside to it. If the “program,” execution for which is being proved, uses the…

Mathematics

13 min read

Why and How zk-SNARK Works 5: Variable Polynomials
Why and How zk-SNARK Works 5: Variable Polynomials
Mathematics

13 min read


Apr 11, 2019

Why and How zk-SNARK Works 4: General-Purpose Computation

This is a series of articles. Part 3, ​ PDF version. We have paved our way with a simple yet sufficient example involving most of the zk-SNARK machinery, and it is now possible to advance the scheme to execute zero-knowledge programs. Computation Let us consider a simple program in pseudocode: Algorithm…

Mathematics

11 min read

Why and How zk-SNARK Works 4: General-Purpose Computation
Why and How zk-SNARK Works 4: General-Purpose Computation
Mathematics

11 min read


Apr 9, 2019

Why and How zk-SNARK Works 3: Non-interactivity & Distributed Setup

This is a series of articles. Part 2,​ ​ PDF version Non-Interactivity Till this point, we had an interactive zero-knowledge scheme. Why is that the case? Because the proof is only valid for the original verifier, nobody else (other verifiers) can trust the same proof since: the verifier could collude with…

Blockchain

9 min read

Why and How zk-SNARK Works 3: Non-interactivity & Distributed Setup
Why and How zk-SNARK Works 3: Non-interactivity & Distributed Setup
Blockchain

9 min read


Apr 8, 2019

Why and How zk-SNARK Works 2: Proving Knowledge of a Polynomial

This is a series of articles. Part 1,​ ​ PDF version. We start with a problem of proving the knowledge of a polynomial and make our way to a generic approach. We will discover many other properties of polynomials along the way. The discussion so far has focused on a…

Cryptography

16 min read

Why and How zk-SNARK Works 2: Proving Knowledge of a Polynomial
Why and How zk-SNARK Works 2: Proving Knowledge of a Polynomial
Cryptography

16 min read


Mar 20, 2019

Why and How zk-SNARK Works 1: Introduction & the Medium of a Proof

The article is an adaptation of the PDF version. Despite the existence of multiple great resources on zk-SNARK construction, from original papers [Bit+11; Par+13] to explainers [Rei16; But16; But17; Gab17], due to the sheer number of moving parts the subject remains a black box for many. …

Blockchain

8 min read

Why and How zk-SNARK Works 1: Introduction & the Medium of a Proof
Why and How zk-SNARK Works 1: Introduction & the Medium of a Proof
Blockchain

8 min read


Jan 3, 2018

Game-changing Year for Private Blockchains

A private blockchain is a great way to achieve consensus between independent companies on transactions they do between each other. It brings decentralization into the equation, where no single party is responsible for maintaining master records and running business logic, and therefore has to be trusted. While usually, parties are…

Blockchain

4 min read

Game-changing Year for Private Blockchains
Game-changing Year for Private Blockchains
Blockchain

4 min read


Mar 1, 2017

First Title Deed Registration at EntEth

It was a great and surprisingly very welcoming experience to demo first ever Title Deed registration on the Quorum blockchain. Other physical objects such as a bar of gold and a package for shipment was demoed at Enterprise Ethereum Alliance launch event. Discover how can you give cryptographic identity to any physical object and connect the dots between real world and the blockchain world.

Blockchain

1 min read

Blockchain

1 min read

Maksym

Maksym

449 Followers

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