Awesome zero knowledge proofs (zkp)

A curated list of awesome things related to learning zero knowledge proofs

Contents

• Awesome zero knowledge proofs (zkp)
  • Contents
  • General introduction
  • Courses
  • Use cases
  • Applications
    • Ethereum
    • Other blockchains
    • Non-blockchain
  • Comparison of the most popular zkp systems
  • Bulletproofs
    • Try
    • Proof system implementations
    • Halo
  • SNARKs
    • Learn
    • Try
    • Scaling the prover
    • Multi-Party Ceremony (MPC) for Trusted Setup
  • SNORKs
    • Sonic
    • PLONK
    • Marlin
  • STARKS
    • Learn
    • FRI-STARKs
    • SuperSonic
    • Fractal
  • Social media

General introduction

Zero-Knowledge Proofs Starter Pack: alternative introductory list for beginners (more videos).

• Zero Knowledge Proofs: An illustrated primer by Matthew Green
• Demystifying zero-knowledge proofs (video) (math-heavy, awesome introduction into underlying cryptography)
• Introduction to SNARKs/STARKs by Eli Ben-Sasson (YouTube)
• On Interactive Proofs and Zero-Knowledge: A Primer
• ZK Basics Cheatsheet - a "for (not too much) dummies" poster, trying to not miss core concepts despite the simplified approach and topics selection
• A Non-Mathematical Introduction to Zero Knowledge Proof - a ZKP primer for those who flunked algebra

ZK whiteboard sessions by ZK Hack:

• Part 1: What is a SNARK?
• Part 2: Building a SNARK (Part I):
• Part 3: Building a SNARK (Part 2)
• Part 4: SNARKS vs. STARKS
• Part 5: PLONK and Custom Gates with Adrian Hamelink
• Part 6: Lookup Arguments for Performance Optimisation
• Part 7: Zero Knowledge Virtual Machines (zkVM)
• Part 8: Achieving Decentralised Private Computation
• Part 9: Introduction to zkRollups

A Hands-On Tutorial for Zero-Knowledge Proofs by Shir Peled (StarkWare):

• Part I
• Part II
• Part III
• Appendix

Zero-Knowledge Proofs for Engineers (Dark Forest)

• Part I
• Part II

More complete curated list of implementations and scientific resources: https://zkp.science

Courses

• The 9th BIU Winter School on Cryptography: Zero Knowledge
• UIUC: ECE498AC/CS498AM: Applied Cryptography, Fall 2019
• Zero Knowledge Proof, MOOC Spring 2023
• [MIT IAP 2023] Modern Zero Knowledge Cryptography

Use cases

• Awesome Privacy on Blockchains

Applications

Ethereum

• ZK Sync by Matter Labs
  • ZK SDK
  • ZK Sync code
  • ZK Sync live demo
• SNARK-based permissioned database: rollup by BarryWhitehat
• Gnosis dFusion: DEX on SNARKs
• Loopring DEX Protocol (v3)
• zkPoD: A Practical Decentralized System for Data Exchange
• Dark Forest: zkSNARK space warfare strategy game

Other blockchains

• Zcash: Privacy-Protecting Digital Currency (SNARKs)
  • Community Chat
  • Forums
• Monero: Private Digital Currency (Bulletproofs)
• Mina Protocol: A Constant-Size Blockchain (recursive SNARKs)
  • YouTube introduction
• Grin: Simple, privacy-focused, scalable MimbleWimble chain implementation (Bulletproofs)
• Beam: Private and Scalable Coin based on MimbleWimble
• Namada: Asset Agnostic, Multichain privacy (SNARKs)
  • Youtube Introduction
  • Specs Documentation

Non-blockchain

• Zero-Knowledge Machine Learning - awesome-zkml
• zk-email
• Proof of Passport
• Semaphore

Comparison of the most popular zkp systems

	SNARKs	STARKs	Bulletproofs
Algorithmic complexity: prover	O(N * log(N))	O(N * poly-log(N))	O(N * log(N))
Algorithmic complexity: verifier	~O(1)	O(poly-log(N))	O(N)
Communication complexity (proof size)	~O(1)	O(poly-log(N))	O(log(N))
- size estimate for 1 TX	Tx: 200 bytes, Key: 50 MB	45 kB	1.5 kb
- size estimate for 10.000 TX	Tx: 200 bytes, Key: 500 GB	135 kb	2.5 kb
Ethereum/EVM verification gas cost	~600k (Groth16)	~2.5M (estimate, no impl.)	N/A
Trusted setup required?	YES 😒	NO 😄	NO 😄
Post-quantum secure	NO 😒	YES 😄	NO 😒
Crypto assumptions	DLP + secure bilinear pairing 😒	Collision resistant hashes 😄	Discrete log 😏

Bulletproofs

• Introduction and collection of resources
• From Zero (Knowledge) to Bulletproofs - a long and very nice gradual explanation
• Bulletproofs - succinct and complete description of the protocol

Try

• Implementation in Haskell
• Implementation in Rust
• Implementation in C

Proof system implementations

• Programmable Constraint Systems for Bulletproofs

Halo

• Halo: Recursive bullet proof composition

SNARKs

SNARK = Succinct Non-interactive ARguments of Knowledge

Learn

Get started:

• Introduction to zk-SNARKs with examples
• What are zk-SNARKs (Zcash blog)
• BabySNARK- The simplest possible SNARK for NP. You know, for kids!
• The MoonMath Manual to zk-SNARKs (A free learning resource for beginners to experts)

Why and How zk-SNARK Works:

• Why and How zk-SNARK Works 1: Introduction & the Medium of a Proof
• Why and How zk-SNARK Works 2: Proving Knowledge of a Polynomial
• Why and How zk-SNARK Works 3: Non-interactivity & Distributed Setup
• Why and How zk-SNARK Works 4: General-Purpose Computation
• Why and How zk-SNARK Works 5: Variable Polynomials
• Why and How zk-SNARK Works 6: Verifiable Computation Protocol
• Why and How zk-SNARK Works 7: Constraints and Public Inputs
• Why and How zk-SNARK Works 8: Zero-Knowledge Computation

ZkStudyClub:

• ZkStudyClub Part 1: Polynomial Commitments with Justin Drake
• ZkStudyClub Part 2: Polynomial Commitments with Justin Drake
• ZkStudyClub Part 3: Polynomial Commitments with Justin Drake

Electric Coin blog series:

• Explaining SNARKs Part I: Homomorphic Hidings
• Explaining SNARKs Part II: Blind Evaluation of Polynomials
• Explaining SNARKs Part III: The Knowledge of Coefficient Test and Assumption
• Explaining SNARKs Part IV: How to make Blind Evaluation of Polynomials Verifiable
• Explaining SNARKs Part V: From Computations to Polynomials
• Explaining SNARKs Part VI: The Pinocchio Protocol
• Explaining SNARKs Part VII: Pairings of Elliptic Curves

Vitalik Buterin's blog series on SNARKs:

• Part 1: Quadratic Arithmetic Programs: from Zero to Hero
• Part 2: Exploring Elliptic Curve Pairings
• Part 3: Zk-SNARKs: Under the Hood

Protocol descriptions:

• zkSNARKs in a Nutshell
• Groth16 protocol (original paper)
• Zcash Sapling protocol spec (very useful as detailed cheat-sheet of all cryptography used)

Try

• libsnark (C++)
  • great tutorial
• bellman (rust)
  • demo circuit
• jsnark (Java, bindings to libsnark)
• snarky (Ocaml, from O(1) labs, team behind Mina Protocol)
• zokrates (toolbox for zkSNARKs on Ethereum)
  • ZoKrates Remix plugin tutorial
  • Zero Knowledge Proof Application Demo, with libsnarks, truffle and docker
• ethsnarks by HarryR (alternative toolkit for viable zk-SNARKS on Ethereum, Web, Mobile and Desktop)
• gnark - library for zero-knowledge proof protocols written in Go
• circom and snarkjs tutorial
  • Roll-up tutorial using Circom and SnarkJS by Ying Tong
  • A circuit and zk-snark implement using Circom and SnarkJS by Luozhu
• SnarkyJS - a TypeScript framework for writing zk-SNARKs in the browser and developing Snapps for Mina Protocol by O(1) labs - WIP

Scaling the prover

• DIZK: Java library for distributed zero knowledge proof systems with Apache Spark (see the research paper)
• SnarkyGPU: distributed GPU based zkSNARKs prover (work in progress)

Multi-Party Ceremony (MPC) for Trusted Setup

• “Powers of Tau” protocol for scalable generation of structured reference string
• Implementation of ZCash MPC Ceremony, Part I: "Powers of Tau"
  • Archived independent implementation in Go
• Implementation of ZCash MPC Ceremony, Part I: "Sapling Circuit"

SNORKs

SNORK = Succinct Non-interactive Oecumenical (Universal) aRguments of Knowledge

SNORKs are SNARKs with universal and updateable trusted setup.

Sonic

• Introducing Sonic: A Practical zk-SNARK with a Nearly Trustless Setup
• Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updateable Structured Reference Strings
• Sonic MPC implementation by Matter Labs

PLONK

(This is a recent development. Contributions are welcome!)

• Awesome PLONK: A curated list of awesome things related to plonk proof system.
• Understanding PLONK by Vitalik Buterin
• Ignition: Trusted Setup MPC Ceremony for PLONK
• Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge

Marlin

(This is a recent development. Contributions are welcome!)

• A Marlin is One of the Fastest SNARKs in the Ocean
• Marlin: Preprocessing zkSNARKs with Universal and Updatable SRS

STARKS

STARK = Succinct (Scalable) Transparent ARguments of Knowledge

STARKs are SNARKs without Trusted Setup.

Learn

Get started:

• STARK @ Home {video playlist}

FRI-STARKs

Introduction:

• Transparent Succinct Arguments by Alessandro Chiesa (Oct 2018)
• State of the STARK by Eli Ben-Sasson (Devcon IV, Oct 2018) (video)
• Introduction to ZK-STARKs by [email protected]

Vitalik Buterin's blog series on STARKs:

• Part I: Proofs with Polynomials
• Part II: Thank Goodness It's FRI-day
• Part III: Into the Weeds

Academic resources:

• The STARK paper
• libstark implementation

More resources available at starkware.co

SuperSonic

(This is a recent development. Contributions are welcome!)

• Transparent SNARKs from DARK Compilers (Dec 2019)
• Introducing Sonic: A Practical zk-SNARK with a Nearly Trustless Setup

Fractal

(This is a recent development. Contributions are welcome!)

• Fractal: Post-Quantum and Transparent Recursive Proofs from Holography

Social media

Stay tuned!

• Awesome zero knowledge twitter list
• Zero-knowledge podcast
• ZKProof, an academic and industry initiative for standardizing Zero Knowledge Proofs