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What is Zero-Knowledge?

Basic explanations and intuitive overviews of Zero-Knowledge Proofs.

Zero Knowledge Proofs MOOC, Spring 2023 External Link Recommended

A online MOOC from University of California, Berkeley.

A beginner's intro to coding zero-knowledge proofs External Link

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 External Link Recommended

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

Prerequisite understanding questions External Link

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

Understanding ZKPs Through Illustrated Examples External Link

Visual explanations of zero-knowledge proofs using everyday examples.

Understanding zero-knowledge proofs without cryptography background External Link

A guide to understanding ZKPs without requiring deep cryptography knowledge.

A Non-Mathematical Introduction to Zero Knowledge Proof External Link

An accessible introduction to ZKPs without heavy mathematics.

Zero Knowledge Proofs: An Illustrated Primer External Link

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

What are zk-SNARKs? External Link

An explanation of zk-SNARKs from the Zcash team.

ZKPs for Engineers: Introduction External Link

A technical but accessible introduction to ZKPs for engineers.

zkSNARKs in a nutshell External Link

A concise explanation of zkSNARKs from the Ethereum blog.

The RareSkills Book of Zero Knowledge External Link

A comprehensive book on zero-knowledge proofs.

An approximate introduction to how zk-SNARKs are possible External Link

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

Privacy in Cryptocurrencies: An Overview External Link

An overview of privacy technologies in cryptocurrencies, including ZKPs.

Zero Knowledge virtual machine step by step External Link

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

Comments on paper: zkSNARKs in a Nutshell by Aaron External Link

Detailed comments and explanations on a key zkSNARK paper.

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Mathematical Foundations

Essential mathematics and cryptography resources for understanding ZK proofs.

Introduction to Mathematical Cryptography External Link

Comprehensive textbook covering the mathematical foundations of cryptography.

Modern Computer Algebra External Link

Textbook on computer algebra, essential for understanding ZK implementations.

Explicit-Formulas Database External Link

Collection of formulas for efficient implementation of elliptic curve operations.

Abstract Algebra External Link

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

Computational Introduction to Number Theory and Algebra External Link

Accessible introduction to number theory and algebra with computational focus.

A Graduate Course in Applied Cryptography External Link

Comprehensive cryptography textbook from Stanford professors.

Elliptic Curves: Number Theory And Cryptography External Link

Deep dive into elliptic curves and their applications in cryptography.

Pairings for Beginners External Link

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

The MoonMath Manual to zk-SNARKs External Link

Accessible introduction to the mathematics behind zk-SNARKs.

Explaining SNARKs Series External Link

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

Proofs, Arguments, and Zero-Knowledge External Link

Comprehensive textbook on interactive proofs and zero-knowledge.

Succinct Proofs and Linear Algebra External Link

Research paper connecting linear algebra to succinct proof systems.

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Beginner-Friendly Tools

Tools and playgrounds to help beginners start experimenting with ZK.

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Online Playgrounds

Interactive online environments to experiment with ZK circuits without installation.

ZKrepl External Link

An online REPL for Circom circuits.

Halo2 REPL External Link

Interactive environment for Halo2 circuit development.

Plonk Pro External Link

Online playground for PLONKish ZK circuits (halo2/plonky3).

Gnark Playground External Link

Interactive environment for Gnark circuit development.

ZK Accel Playground External Link

Interactive playground for ZK circuit development.