Beginner Learning
Getting started with zero-knowledge proofs
What is Zero-Knowledge?
Basic explanations and intuitive overviews of Zero-Knowledge Proofs.
Zero Knowledge Proofs MOOC, Spring 2023
Recommended
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, Compilers
Recommended
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.
Mathematical Foundations
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.
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.
Beginner-Friendly Tools
Tools and playgrounds to help beginners start experimenting with ZK.
Online Playgrounds
Interactive online environments to experiment with ZK circuits without installation.
ZKrepl
An online REPL for Circom circuits.
Halo2 REPL
Interactive environment for Halo2 circuit development.
Plonk Pro
Online playground for PLONKish ZK circuits (halo2/plonky3).
Gnark Playground
Interactive environment for Gnark circuit development.
ZK Accel Playground
Interactive playground for ZK circuit development.