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https://github.com/matter-labs/awesome-zero-knowledge-proofs

A curated list of awesome things related to learning Zero-Knowledge Proofs (ZKP).
https://github.com/matter-labs/awesome-zero-knowledge-proofs

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A curated list of awesome things related to learning Zero-Knowledge Proofs (ZKP).

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# Awesome zero knowledge proofs (zkp)



> [![Awesome](https://awesome.re/badge.svg)](https://awesome.re)

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



## Contents



- [Awesome zero knowledge proofs (zkp)](#awesome-zero-knowledge-proofs-zkp)

  - [Contents](#contents)

  - [General introduction](#general-introduction)

  - [Courses](#courses)

  - [Use cases](#use-cases)

  - [Applications](#applications)

    - [Ethereum](#ethereum)

    - [Other blockchains](#other-blockchains)

    - [Non-blockchain](#non-blockchain)

  - [Comparison of the most popular zkp systems](#comparison-of-the-most-popular-zkp-systems)

  - [Bulletproofs](#bulletproofs)

    - [Try](#try)

    - [Proof system implementations](#proof-system-implementations)

    - [Halo](#halo)

  - [SNARKs](#snarks)

    - [Learn](#learn)

    - [Try](#try-1)

    - [Scaling the prover](#scaling-the-prover)

    - [Multi-Party Ceremony (MPC) for Trusted Setup](#multi-party-ceremony-mpc-for-trusted-setup)

  - [SNORKs](#snorks)

    - [Sonic](#sonic)

    - [PLONK](#plonk)

    - [Marlin](#marlin)

  - [STARKS](#starks)

    - [Learn](#learn-1)

    - [FRI-STARKs](#fri-starks)

    - [SuperSonic](#supersonic)

    - [Fractal](#fractal)

  - [Social media](#social-media)



## General introduction



[Zero-Knowledge Proofs Starter Pack](https://ethresear.ch/t/zero-knowledge-proofs-starter-pack/4519): alternative introductory list for beginners (more videos).



- [Zero Knowledge Proofs: An illustrated primer by Matthew Green](https://blog.cryptographyengineering.com/2014/11/27/zero-knowledge-proofs-illustrated-primer/)

- [Demystifying zero-knowledge proofs](https://docs.google.com/presentation/d/1gfB6WZMvM9mmDKofFibIgsyYShdf0RV_Y8TLz3k1Ls0/edit#slide=id.p) ([video](https://www.youtube.com/watch?v=_6TqUNVLChc)) (math-heavy, awesome introduction into underlying cryptography)

- [Introduction to SNARKs/STARKs by Eli Ben-Sasson](https://www.youtube.com/watch?v=VUN35BC11Qw) (YouTube)

- [On Interactive Proofs and Zero-Knowledge: A Primer](https://medium.com/magicofc/interactive-proofs-and-zero-knowledge-b32f6c8d66c3)

- [ZK Basics Cheatsheet](https://github.com/baro77/ZKbasicsCS) - 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](https://mirror.xyz/krinza.eth/5_Cr91cBK3XdkeHPQ9yjc7z_4NoTNxyqBiM4Jz4d5VE) - a ZKP primer for those who flunked algebra



[ZK whiteboard sessions by ZK Hack](https://zkhack.dev/whiteboard/):



- [Part 1: What is a SNARK?](https://zkhack.dev/whiteboard/module-one/)

- [Part 2: Building a SNARK (Part 1):](https://zkhack.dev/whiteboard/module-two/)

- [Part 3: Building a SNARK (Part 2)](https://zkhack.dev/whiteboard/module-three/)

- [Part 4: SNARKS vs. STARKS](https://zkhack.dev/whiteboard/module-four/)

- [Part 5: PLONK and Custom Gates with Adrian Hamelink](https://zkhack.dev/whiteboard/module-five/)

- [Part 6: Lookup Arguments for Performance Optimisation](https://zkhack.dev/whiteboard/module-six/)

- [Part 7: Zero Knowledge Virtual Machines (zkVM)](https://zkhack.dev/whiteboard/module-seven/)

- [Part 8: Achieving Decentralised Private Computation](https://zkhack.dev/whiteboard/module-eight/)

- [Part 9: Introduction to zkRollups](https://zkhack.dev/whiteboard/module-nine/)



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



- [Part I](https://www.shirpeled.com/2018/09/a-hands-on-tutorial-for-zero-knowledge.html)

- [Part II](https://www.shirpeled.com/2018/10/a-hands-on-tutorial-for-zero-knowledge.html)

- [Part III](https://www.shirpeled.com/2018/10/a-hands-on-tutorial-for-zero-knowledge_2.html)

- [Appendix](https://www.shirpeled.com/2018/10/a-hands-on-tutorial-for-zero-knowledge_4.html)



Zero-Knowledge Proofs for Engineers (Dark Forest)



- [Part I](https://blog.zkga.me/intro-to-zksnarks)

- [Part II](https://blog.zkga.me/df-init-circuit)



More complete curated list of implementations and scientific resources:

[https://zkp.science](https://zkp.science)



## Courses



- [The 9th BIU Winter School on Cryptography: Zero Knowledge](https://cyber.biu.ac.il/event/the-9th-biu-winter-school-on-cryptography/)

- [UIUC: ECE498AC/CS498AM: Applied Cryptography, Fall 2019](http://soc1024.ece.illinois.edu/teaching/ece498ac/fall2019/)

- [Zero Knowledge Proof, MOOC Spring 2023](https://zk-learning.org/)

- [[MIT IAP 2023] Modern Zero Knowledge Cryptography](https://zkiap.com/)



## Use cases



- [Awesome Privacy on Blockchains](https://github.com/Mikerah/awesome-privacy-on-blockchains)



## Applications



### Ethereum



- [ZK Sync](https://medium.com/matter-labs/introducing-zk-sync-the-missing-link-to-mass-adoption-of-ethereum-14c9cea83f58) by [Matter Labs](https://matter-labs.io)

  - [ZK SDK](https://zksync.io)

  - [ZK Sync code](https://github.com/matter-labs/zksync)

- [SNARK-based permissioned database: rollup by BarryWhitehat](https://github.com/barryWhiteHat/roll_up)

- [Gnosis dFusion: DEX on SNARKs](https://github.com/gnosis/dex-research/tree/master/dFusion)

- [Loopring DEX Protocol (v3)](https://github.com/Loopring/protocols/blob/master/packages/loopring_v3/DESIGN.md)

- [zkPoD: A Practical Decentralized System for Data Exchange](https://github.com/sec-bit/zkPoD-node)

- [Dark Forest: zkSNARK space warfare strategy game](https://zkga.me/)



### Other blockchains



- [Zcash: Privacy-Protecting Digital Currency](https://z.cash) (SNARKs)

  - [Community Chat](https://discord.com/invite/zcash)

  - [Forums](https://forum.zcashcommunity.com)

- [Monero: Private Digital Currency](https://www.getmonero.org) (Bulletproofs)

- [Mina Protocol: A Constant-Size Blockchain](https://minaprotocol.com/) (recursive SNARKs)

  - [YouTube introduction](https://www.youtube.com/watch?v=qCVACpgQSjo)

- [Grin: Simple, privacy-focused, scalable MimbleWimble chain implementation](https://grin.mw/) (Bulletproofs)

- [Beam: Private and Scalable Coin based on MimbleWimble](https://www.beam.mw)

- [Namada: Asset Agnostic, Multichain privacy](https://namada.net/) (SNARKs)

  - [Youtube Introduction](https://youtu.be/F2cPd7nwG7A?si=iHw93A3ziLc9neH5)

  - [Specs Documentation](https://specs.namada.net/masp)

- [IronFish: Privacy-Preserving Regulatory-Friendly Cryptocurrency Platform](https://ironfish.network/use/get-started/get-started) (Groth16 zk-SNARKs)

  - [Whitepaper](https://ironfish.network/learn/whitepaper)

  - [Community Chat](https://discord.ironfish.network/)

  - [YouTube Channel](https://www.youtube.com/@ironfishnetwork)

- [succinct: Write ZKPs with Rust using SP1, a performant, open-source zkVM and generate proofs in 1-click on Succinct’s decentralized prover network](https://succinct.xyz/)

  - [document](https://succinctlabs.github.io/sp1/)

- [Valida： Valida is a STARK-based virtual machine，The VM has a RISC-inspired instruction set，The VM is designed to be customizable. It can easily be extended to include an arbitrary number of user-defined instructions](https://github.com/valida-xyz/valida)

- [Nexus zkVM:  Nexus is a modular, extensible, open-source, highly-parallelized, prover-optimized, contributor-friendly, zkVM written in Rust, focused on performance and security.](https://nexus.xyz/)



### Non-blockchain



- Zero-Knowledge Machine Learning - [awesome-zkml](https://github.com/worldcoin/awesome-zkml)

- [zk-email](https://github.com/zkemail)

- [Proof of Passport](https://github.com/zk-passport/proof-of-passport)

- [Semaphore](https://github.com/semaphore-protocol/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 :unamused:             | NO :smile:                    | NO :smile:      |

| Post-quantum secure                   | NO :unamused:              | YES :smile:                   | NO :unamused:   |

| Crypto assumptions                    | DLP + secure bilinear pairing :unamused:          | Collision resistant hashes :smile: | Discrete log :smirk: |



## Bulletproofs



- [Introduction and collection of resources](https://crypto.stanford.edu/bulletproofs/)

- [From Zero (Knowledge) to Bulletproofs](https://github.com/AdamISZ/from0k2bp) - a long and very nice gradual explanation

- [Bulletproofs](http://sikoba.com/docs/SKOR_DK_Bulletproofs_201905.pdf) - succinct and complete description of the protocol



### Try



- [Implementation in Haskell](https://github.com/adjoint-io/bulletproofs)

- [Implementation in Rust](https://github.com/dalek-cryptography/bulletproofs)

- [Implementation in C](https://github.com/Tongsuo-Project/Tongsuo)



### Proof system implementations



- [Programmable Constraint Systems for Bulletproofs](https://medium.com/interstellar/programmable-constraint-systems-for-bulletproofs-365b9feb92f7)



### Halo



- [Halo: Recursive bullet proof composition](https://www.coindesk.com/you-can-now-prove-a-whole-blockchain-with-one-math-problem-really)



## SNARKs



> SNARK = **S**uccinct **N**on-interactive **AR**guments of **K**nowledge



### Learn



Get started:



- [Introduction to zk-SNARKs with examples](https://consensys.io/blog/introduction-to-zk-snarks)

- [What are zk-SNARKs (Zcash blog)](https://z.cash/technology/zksnarks)

- [BabySNARK- The simplest possible SNARK for NP. You know, for kids!](https://github.com/initc3/babySNARK)

- [The MoonMath Manual to zk-SNARKs (A free learning resource for beginners to experts)](https://leastauthority.com/community-matters/moonmath-manual/)



Why and How zk-SNARK Works:



- [Why and How zk-SNARK Works 1: Introduction & the Medium of a Proof](https://medium.com/@imolfar/why-and-how-zk-snark-works-1-introduction-the-medium-of-a-proof-d946e931160)

- [Why and How zk-SNARK Works 2: Proving Knowledge of a Polynomial](https://medium.com/@imolfar/why-and-how-zk-snark-works-2-proving-knowledge-of-a-polynomial-f817760e2805)

- [Why and How zk-SNARK Works 3: Non-interactivity & Distributed Setup](https://medium.com/@imolfar/why-and-how-zk-snark-works-3-non-interactivity-distributed-setup-c0310c0e5d1c)

- [Why and How zk-SNARK Works 4: General-Purpose Computation](https://medium.com/@imolfar/why-and-how-zk-snark-works-4-general-purpose-computation-dcdc8081ee42)

- [Why and How zk-SNARK Works 5: Variable Polynomials](https://medium.com/@imolfar/why-and-how-zk-snark-works-5-variable-polynomials-3b4e06859e30)

- [Why and How zk-SNARK Works 6: Verifiable Computation Protocol

](https://medium.com/@imolfar/why-and-how-zk-snark-works-6-verifiable-computation-protocol-1aa19f95a5cc)

- [Why and How zk-SNARK Works 7: Constraints and Public Inputs](https://medium.com/@imolfar/why-and-how-zk-snark-works-7-constraints-and-public-inputs-e95f6596dd1c)

- [Why and How zk-SNARK Works 8: Zero-Knowledge Computation](https://medium.com/@imolfar/why-and-how-zk-snark-works-8-zero-knowledge-computation-f120339c2c55)



ZkStudyClub:



- [ZkStudyClub Part 1: Polynomial Commitments with Justin Drake](https://www.youtube.com/watch?v=bz16BURH_u8)

- [ZkStudyClub Part 2: Polynomial Commitments with Justin Drake](https://www.youtube.com/watch?v=BfV7HBHXfC0)

- [ZkStudyClub Part 3: Polynomial Commitments with Justin Drake](https://www.youtube.com/watch?v=TbNauD5wgXM)



Electric Coin blog series:



- [Explaining SNARKs Part I: Homomorphic Hidings](https://electriccoin.co/blog/snark-explain/)

- [Explaining SNARKs Part II: Blind Evaluation of Polynomials](https://electriccoin.co/blog/snark-explain2/)

- [Explaining SNARKs Part III: The Knowledge of Coefficient Test and Assumption](https://electriccoin.co/blog/snark-explain3/)

- [Explaining SNARKs Part IV: How to make Blind Evaluation of Polynomials Verifiable](https://electriccoin.co/blog/snark-explain4/)

- [Explaining SNARKs Part V: From Computations to Polynomials](https://electriccoin.co/blog/snark-explain5/)

- [Explaining SNARKs Part VI: The Pinocchio Protocol](https://electriccoin.co/blog/snark-explain6/)

- [Explaining SNARKs Part VII: Pairings of Elliptic Curves](https://electriccoin.co/blog/snark-explain7/)



Vitalik Buterin's blog series on SNARKs:



- [Part 1: Quadratic Arithmetic Programs: from Zero to Hero](https://medium.com/@VitalikButerin/quadratic-arithmetic-programs-from-zero-to-hero-f6d558cea649)

- [Part 2: Exploring Elliptic Curve Pairings](https://medium.com/@VitalikButerin/exploring-elliptic-curve-pairings-c73c1864e627)

- [Part 3: Zk-SNARKs: Under the Hood](https://medium.com/@VitalikButerin/zk-snarks-under-the-hood-b33151a013f6)



Protocol descriptions:



- [zkSNARKs in a Nutshell](https://chriseth.github.io/notes/articles/zksnarks/zksnarks.pdf)

- [Groth16 protocol](https://eprint.iacr.org/2016/260.pdf) (original paper)

- [Zcash Sapling protocol spec](https://github.com/zcash/zips/blob/master/protocol/protocol.pdf) (very useful as detailed cheat-sheet of all cryptography used)



OxPARC learning group:



- [Circom](https://learn.0xparc.org/circom)

- [Halo2](https://learn.0xparc.org/halo2)



### Try



- [libsnark (C++)](https://github.com/scipr-lab/libsnark)

  - [great tutorial](https://github.com/christianlundkvist/libsnark-tutorial)

- [bellman (rust)](https://github.com/zkcrypto/bellman/)

  - [demo circuit](https://github.com/ebfull/bellman-demo)

- [jsnark (Java, bindings to libsnark)](https://github.com/akosba/jsnark)

- [snarky (Ocaml, from O(1) labs, team behind Mina Protocol)](https://github.com/o1-labs/snarky)

- [zokrates (toolbox for zkSNARKs on Ethereum)](https://github.com/Zokrates/ZoKrates)

  - [ZoKrates Remix plugin tutorial](https://medium.com/coinmonks/zokrates-zksnarks-on-ethereum-made-easy-8022300f8ba6)

  - [Zero Knowledge Proof Application Demo, with libsnarks, truffle and docker](https://medium.com/hackernoon/zero-knowledge-proof-application-demo-2a457cfc73c1)

- [ethsnarks by HarryR (alternative toolkit for viable zk-SNARKS on Ethereum, Web, Mobile and Desktop)](https://github.com/HarryR/ethsnarks)

- [gnark - library for zero-knowledge proof protocols written in Go](https://github.com/ConsenSys/gnark)

- [circom and snarkjs tutorial](https://github.com/iden3/circom_old/blob/master/TUTORIAL.md)

  - [Roll-up tutorial using Circom and SnarkJS by Ying Tong](https://github.com/therealyingtong/roll_up_circom_tutorial)

  - [A circuit and zk-snark implement using Circom and SnarkJS by Luozhu](https://github.com/LuozhuZhang/zkps-circuit-snark)

- [SnarkyJS - a TypeScript framework for writing zk-SNARKs in the browser and developing Snapps for Mina Protocol by O(1) labs - WIP](https://github.com/o1-labs/snarkyjs)



### Scaling the prover



- [DIZK: Java library for distributed zero knowledge proof systems with Apache Spark](https://github.com/scipr-lab/dizk) (see the [research paper](https://eprint.iacr.org/2018/691))

- [SnarkyGPU: distributed GPU based zkSNARKs prover](https://github.com/matterinc/snarkyGPU) (work in progress)



### Multi-Party Ceremony (MPC) for Trusted Setup



- [“Powers of Tau” protocol for scalable generation of structured reference string](https://eprint.iacr.org/2017/1050)

- [Implementation of ZCash MPC Ceremony, Part I: "Powers of Tau"](https://github.com/ebfull/powersoftau)

  - [Archived independent implementation in Go](https://github.com/FiloSottile/powersoftau/)

- [Implementation of ZCash MPC Ceremony, Part I: "Sapling Circuit"](https://github.com/zcash-hackworks/sapling-mpc)



## SNORKs



> SNORK = **S**uccinct **N**on-interactive **O**ecumenical (Universal) a**R**guments of **K**nowledge



SNORKs are SNARKs with universal and updateable trusted setup.



### Sonic



- [Introducing Sonic: A Practical zk-SNARK with a Nearly Trustless Setup](https://www.benthamsgaze.org/2019/02/07/introducing-sonic-a-practical-zk-snark-with-a-nearly-trustless-setup/)

- [Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updateable Structured Reference Strings](https://eprint.iacr.org/2019/099)

- [Sonic MPC implementation by Matter Labs](https://github.com/matter-labs/alpha_line)



### PLONK



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



- [Awesome PLONK](https://github.com/Fluidex/awesome-plonk): A curated list of awesome things related to plonk proof system.

- [Understanding PLONK by Vitalik Buterin](https://vitalik.eth.limo/general/2019/09/22/plonk.html)

- [Ignition: Trusted Setup MPC Ceremony for PLONK](https://medium.com/aztec-protocol/aztec-announcing-our-ignition-ceremony-757850264cfe)

- [Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of Knowledge](https://eprint.iacr.org/2019/953.pdf)



### Marlin



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



- [A Marlin is One of the Fastest SNARKs in the Ocean](https://www.benthamsgaze.org/2019/09/19/a-marlin-is-one-of-the-fastest-snarks-in-the-ocean/)

- [Marlin: Preprocessing zkSNARKs with Universal and Updatable SRS](https://eprint.iacr.org/2019/1047.pdf)



## STARKS



> STARK = **S**uccinct (**S**calable) **T**ransparent **AR**guments of **K**nowledge



STARKs are SNARKs without Trusted Setup.



### Learn



Get started:



- [STARK @ Home {video playlist}](https://www.youtube.com/playlist?list=PLcIyXLwiPilUFGw7r2uyWerOkbx4GFMXq)



### FRI-STARKs



Introduction:



- [Transparent Succinct Arguments by Alessandro Chiesa (Oct 2018)](https://gist.github.com/Haseeb-Qureshi/f552fdbbb649ed4bbfeb681beb4091e1)

- [State of the STARK by Eli Ben-Sasson (Devcon IV, Oct 2018)](https://drive.google.com/file/d/1Osa0MXu-04dfwn1YOSgN6CXOgWnsp-Tu/view) ([video](https://www.youtube.com/watch?v=1KSwVIZ82hs))

- [Introduction to ZK-STARKs by [email protected]](https://hackmd.io/s/rJHYnQ3Z4)



Vitalik Buterin's blog series on STARKs:



- [Part I: Proofs with Polynomials](https://vitalik.eth.limo/general/2017/11/09/starks_part_1.html)

- [Part II: Thank Goodness It's FRI-day](https://vitalik.eth.limo/general/2017/11/22/starks_part_2.html)

- [Part III: Into the Weeds](https://vitalik.eth.limo/general/2018/07/21/starks_part_3.html)



Academic resources:



- [The STARK paper](https://eprint.iacr.org/2018/046.pdf)

- [libstark implementation](https://github.com/elibensasson/libSTARK)



More resources available at [starkware.co](https://www.starkware.co)



### SuperSonic



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



- [Transparent SNARKs from DARK Compilers (Dec 2019)](https://eprint.iacr.org/2019/1229.pdf)

- [Introducing Sonic: A Practical zk-SNARK with a Nearly Trustless Setup](https://www.benthamsgaze.org/2019/02/07/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](https://eprint.iacr.org/2019/1076)



## Social media



Stay tuned!



- [Awesome zero knowledge twitter list](https://twitter.com/gluk64/lists/awesome-zkp)

- [Zero-knowledge podcast](https://www.zeroknowledge.fm)

- [ZKProof, an academic and industry initiative for standardizing Zero Knowledge Proofs](https://zkproof.org/)