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This is a series of articles. Part 7,​ ​ PDF version

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…

This is a series of articles. Part 6,​ ​ PDF version


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…

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. …

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…

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.


Let us consider a simple program in pseudocode:


This is a series of articles. Part 2,​ ​ PDF version


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…

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…

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. …

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…

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.

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