
Most explanations struggle to clarify how and why they work, so zk-SNARKs remain somewhat “magical” and elusive, deterring developers from exploring or utilizing them in projects. Resources are scattered across blog posts and GitHub libraries. This results in a high barrier to entry, thereby slowing the widespread adoption of zk-SNARKs and associated privacy-enhancing technologies. Even worse, implementing zk-SNARKs without understanding the fundamentals of how they work increases the potential for security issues.

We want to change that with our MoonMath Manual to zk-SNARKs, designed for an audience with only minimal experience in cryptography and programming.

What is particularly unique about the MoonMath Manual is that it is designed to enable users to construct zk-SNARKs using simple pen-and-paper computations. Throughout the manual, users are encouraged to complete exercises that ensure they engage with the foundational building blocks of zk-SNARKs. While doing that, readers build the smallest possible — but fully functional — cryptographic stack to compute zk-SNARK internals without the need of a computer.

As users go through the manual, they will grasp mathematical concepts that are not only used in SNARKs, but also in other zero-knowledge proofs and cryptography more generally.


The MoonMath Manual is a resource for anyone interested in understanding and unlocking the potential of zk-SNARKs

The MoonMath Manual


## Introductory Modules

- What is a SNARK?
- Building a SNARK (part 1)
- Building a SNARK (part 2)

## Whiteboard Sessions with ZK Projects​

- SNARKs vs. STARKS with Brendan and Bobbin
- PLONK and Custom Gates with Adrian Hamelink
- Lookup Arguments for Performance Optimisation with Mary Maller
- Zero Knowledge Virtual Machine (zkVM) with grjte
- Achieving Decentralised Private Computation with Pratyush Mishra
- Introduction to zkRollups with Barry Whitehat
- zkEVM with Jordi Baylina
- ZK Swaps with Henry de Valence
- zkID with Oleksandr Brezhniev
- Fast Recursion with Plonky2 with William Borgeaud

ZK Whiteboard Sessions is an educational series on all things zero knowledge

ZK Whiteboard Sessions

Free resources to learn about Zero Knowledge Proofs (ZKPs) and Cryptography

Road to ZK

This is a reference repo to help you get started with writing zero-knowledge circuits with Noir

Noir Starters


The easiest way to integrate succinct verifiable on-chain computation using hidden information in custom applications that execute on a credibly-neutral immutable public ledger.

Essentially, it's zero knowledge for those with zero knowledge.

zero knowledge for those with zero knowledge

zk-starter


Magic technology, advancing civilization, short letters, privacy, and a future that's already here. That's Zero Knowledge Proofs (ZKPs) in a nutshell. What's going on?

Zero Knowledge Proofs are magic. They allow us to do things we couldn't dream of before.

A Friendly Introduction to Zero Knowledge

This article walks you through how to build a zk-circuit using the halo2 rust crate by the Zcash team.

Constructing ZK SNARK Circuits


You know how data structures and algorithms are pretty much Computer Science 101? They’re fundamental to just about everything in the field. Well, polynomials are just as fundamental to zero knowledge proofs (ZKPs).

In case you need a primer, ZKPs let us prove a fact without revealing the fact. You can read my [ZKP 101 post](https://www.zkcamp.xyz/blog/what-is-a-zkp-anyway) for all the details. But before we get into level 201, there’s a bit of math and cryptography we should cover.

In this blog post, we’ll focus on the math that makes ZKPs possible: Polynomials. Why? Because they’re really helpful in three major ways:

- They can encode an unbounded amount of data
- They can encode relationships between data
- They let us efficiently check whether two pieces of data are the same


You can't understand ZKPs without understanding polynomials

Polynomials 101


## Overview

Privacy is a fundamental need for many blockchain applications. This tutorial explores how to implement private transactions on Solana using zero-knowledge proofs and shielded pool designs.

Key topics covered:

- Introduction to privacy primitives on Solana
- Understanding shielded pool architecture 
- Implementing deposit and withdrawal functions with ZK proofs
- Managing nullifiers to prevent double-spending
- Creating and verifying zero-knowledge proofs on Solana
- Building a private transaction interface with TypeScript
- Balancing privacy with compliance requirements

Solana's performance characteristics enable privacy solutions that would be too expensive on other chains. This tutorial demonstrates how to build robust privacy-preserving payment systems and applications while leveraging Solana's speed and cost advantages. 

A step-by-step guide to implementing confidential token transfers and transactions on Solana using zero-knowledge proofs and shielded pools.

Building Private Transactions on Solana with Zero-Knowledge


In this series we try to demystify zero-knowledge proofs (ZKPs) for the rest of non-math nerds. Since writing [part 1](https://dev.to/tonyolendo/the-complete-full-stack-guide-to-getting-started-with-zero-knowledge-proofs-using-circom-and-zk-snarks-part-1-53gi), my thoughts on the subject have evolved. I’m more drawn to answering the following questions

- Can anyone be a ZK developer?
- Is there a simple path that we can define for anyone to get started in writing ZK circuits?

The simple answer to all the questions above is yes! Most assuredly, yes. How? Just learn [Circom](https://iden3.io/circom) and you’ll be well on your way.


This tutorial series explains the mechanics of the STARK proof system. It is directed towards a technically-inclined audience with knowledge of basic maths and programming.

Anatomy of a STARK

Start building zero-knowledge products without a degree in computer science and math!

Zero-knowledge is easy or the ultimate how-to article

In this article, and the subsequent series, I will be sharing what I have learnt about one of ZKP protocols and one in particular — zkSNARK Groth16.

Under the hood of zkSNARK Groth16 protocol


## Overview

Zero-knowledge proofs (ZKPs) enable privacy and scalability for blockchain applications. This tutorial explores how to implement ZK applications on Solana using Light Protocol and other ZK frameworks.

Key topics covered:

- Understanding ZK proofs and their applications on Solana
- Setting up Light Protocol SDK for Solana development
- Creating ZK circuits for common use cases
- Implementing privacy-preserving transfers and computations
- Verifying ZK proofs within Solana programs
- Optimizing for performance and minimizing proof costs
- Building user interfaces for ZK applications

Solana's high performance and low transaction costs make it an excellent platform for ZK applications. Unlike other blockchains where ZK proofs can be prohibitively expensive, Solana enables practical privacy-preserving applications that remain cost-effective even with complex proofs. 

Learn how to develop privacy-preserving applications using zero-knowledge proofs on Solana with Light Protocol and other ZK frameworks.

Building Zero-Knowledge Applications on Solana


An exploration of MiMC, Poseidon, and Vision/Rescue, along with a deep dive into SNARK and STARK complexity.

ZK-Friendly Hash Functions


What are zero-knowledge proofs? Justin Thaler (a16z crypto, Georgetown University) demystifies key concepts in this rapidly evolving and increasingly important space. This talk sheds light on the fundamentals of zero-knowledge proofs and SNARKS – including how people are using them today, how web3 startups should be thinking about them, and how they might be used in future. 

#zkp

🎓 ZK Whiteboard Sessions

📺 Introduction to ZKP