Learning

Getting started with zero-knowledge proofs

Resources

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What is Zero-Knowledge? Basic explanations and intuitive overviews of Zero-Knowledge Proofs.
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Mathematical & Cryptography Essential mathematics and cryptography resources for understanding ZK proofs.
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Online Playgrounds Interactive online environments to experiment with ZK circuits without installation.
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Visionary Insights Insights about the future of ZK.
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Understanding Proof Systems Dive deeper into SNARKs, STARKs, and other proving systems.
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Knowledge Base A collective of resources for learning ZK thoroughly.
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Cheatsheets Cheatsheets for ZK related works.

🧠 What is Zero-Knowledge?

Basic explanations and intuitive overviews of Zero-Knowledge Proofs.

Zero Knowledge Proofs MOOC, Spring 2023Recommended

A online MOOC from University of California, Berkeley.

A beginner's intro to coding zero-knowledge proofs

This article will cover what a zero-knowledge proof is, how it is used from a developer's perspective, and go through a few languages for writing them.

ZKP Overview: History, Proving Systems, Circuits, CompilersRecommended

A comprehensive overview of zero-knowledge proofs with interactive visualizations.

Prerequisite understanding questions

A set of questions to test your understanding of zero-knowledge proofs prerequisites.

Understanding ZKPs Through Illustrated Examples

Visual explanations of zero-knowledge proofs using everyday examples.

Understanding zero-knowledge proofs without cryptography background

A guide to understanding ZKPs without requiring deep cryptography knowledge.

A Non-Mathematical Introduction to Zero Knowledge Proof

An accessible introduction to ZKPs without heavy mathematics.

Zero Knowledge Proofs: An Illustrated Primer

A visual introduction to the concepts behind zero-knowledge proofs.

What are zk-SNARKs?

An explanation of zk-SNARKs from the Zcash team.

ZKPs for Engineers: Introduction

A technical but accessible introduction to ZKPs for engineers.

zkSNARKs in a nutshell

A concise explanation of zkSNARKs from the Ethereum blog.

The RareSkills Book of Zero Knowledge

A comprehensive book on zero-knowledge proofs.

An approximate introduction to how zk-SNARKs are possible

Vitalik Buterin's explanation of the underlying concepts that make zk-SNARKs possible.

Privacy in Cryptocurrencies: An Overview

An overview of privacy technologies in cryptocurrencies, including ZKPs.

Zero Knowledge virtual machine step by step

A step-by-step guide to understanding zero-knowledge virtual machines.

Comments on paper: zkSNARKs in a Nutshell by Aaron

Detailed comments and explanations on a key zkSNARK paper.

Jack O'Connor: A Zero-Knowledge PCP Theorem

The intersection of ZK and PCP theorems: every NP statement has a polynomial-size proof that is both locally checkable and zero-knowledge.

Zero-Knowledge Proofs Explained in 3 Examples

A simple explanation of zero-knowledge proofs in 3 examples.

📐 Mathematical & Cryptography

Essential mathematics and cryptography resources for understanding ZK proofs.

Introduction to Mathematical Cryptography

Comprehensive textbook covering the mathematical foundations of cryptography.

Modern Computer Algebra

Textbook on computer algebra, essential for understanding ZK implementations.

Explicit-Formulas Database

Collection of formulas for efficient implementation of elliptic curve operations.

Abstract Algebra

Textbook covering group theory, rings, and fields - fundamental to cryptography.

Computational Introduction to Number Theory and Algebra

Accessible introduction to number theory and algebra with computational focus.

A Graduate Course in Applied Cryptography

Comprehensive cryptography textbook from Stanford professors.

Elliptic Curves: Number Theory And Cryptography

Deep dive into elliptic curves and their applications in cryptography.

Pairings for Beginners

Introduction to pairing-based cryptography, essential for many ZK systems.

The MoonMath Manual to zk-SNARKs

Accessible introduction to the mathematics behind zk-SNARKs.

Explaining SNARKs Series

Step-by-step explanation of how SNARKs work from Electric Coin Company.

1Part I: Homomorphic Hidings 2Part II: Blind Evaluation of Polynomials 3Part III: The Knowledge of Coefficient Test and Assumption 4Part IV: How to make Blind Evaluation of Polynomials Verifiable 5Part V: From Computations to Polynomials 6Part VI: The Pinocchio Protocol 7Part VII: Pairings of Elliptic Curves

Proofs, Arguments, and Zero-Knowledge

Comprehensive textbook on interactive proofs and zero-knowledge.

Succinct Proofs and Linear Algebra

Research paper connecting linear algebra to succinct proof systems.

zkMarek Session 1: Elliptic Curves to Verkle Trees

Season 1 of zkMarek aimed at intuitively explaining topics like elliptic curves, ECDSA, trusted setup, KZG and Vector commitments, Blobs, Merkle and Verkle Trees.