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| # Awesome zero knowledge proofs (zkp) | ||
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| > A curated list of awesome things related to learning zero knowledge proofs | ||
| ## Contents | ||
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| - [General introduction](#general-introduction) | ||
| - [Applications](#applications) | ||
| - [Comparison of the most popular zkp systems](#comparison-of-the-most-popular-zkp-systems) | ||
| - [SNARKs](#snarks) | ||
| - [STARKs](#starks) | ||
| - [Bulletproofs](#bulletproofs) | ||
| - [Social media](#social-media) | ||
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| ## General introduction | ||
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| - [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) (math-heavy, awesome introduction into underlying cryptography) | ||
| - [Introduction to SNARKs/STARKs by Eli Ben-Sasson](https://www.youtube.com/watch?v=VUN35BC11Qw) (YouTube) | ||
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| [More complete curated list of implementations and scientific ressources](https://zkp.science) | ||
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| ## Applications | ||
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| ### Active | ||
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| - [Zcash: Privacy-Protecting Digital Currency](https://z.cash) (SNARKs) | ||
| - [Monero: Private Digital Currency](https://www.getmonero.org) (Bulletproofs) | ||
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| ### Work in progress | ||
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| - [Coda: A Constant-Size Blockchain](https://codaprotocol.com) (recursive SNARKs) | ||
| - [YouTube introduction](https://www.youtube.com/watch?v=qCVACpgQSjo) | ||
| - [Grin: Simple, privacy-focused, scalable MimbleWimble chain implementation](http://grin-tech.org) (Bulletproofs) | ||
| - [Rollup: Ethereum Plasma on SNARKs](https://github.com/barryWhiteHat/roll_up) | ||
| - [chatroom on gitter](https://gitter.im/barrywhitehat/roll_up) | ||
| - [Gnosis dFusion: DEX on SNARKs](https://github.com/gnosis/dex-research/tree/master/dFusion) | ||
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| ## Comparison of the most popular zkp systems | ||
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| | | SNARKs | STARKs | Bulletproofs | | ||
| | ------------------------------------: | -------------------------: | ----------------------------: | --------------: | | ||
| | Algoritmic complexity: prover | O(N * log(N)) | O(N * poly-log(N)) | O(N * log(N)) | | ||
| | Algoritmic 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 | Strong :( | Collision resistant hashes :) | Discrete log :) | | ||
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| ## SNARKs | ||
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| ### Learn | ||
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| Get started: | ||
| - [Introduction to zk-SNARKs with examples](https://media.consensys.net/introduction-to-zksnarks-with-examples-3283b554fc3b) | ||
| - [What are zk-SNARKs (Zcash blog)](https://z.cash/technology/zksnarks) | ||
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| Zcash blog series: | ||
| - [Explaining SNARKs Part I: Homomorphic Hidings](https://z.cash/blog/snark-explain/) | ||
| - [Explaining SNARKs Part II: Blind Evaluation of Polynomials](https://z.cash/blog/snark-explain2) | ||
| - [Explaining SNARKs Part III: The Knowledge of Coefficient Test and Assumption](https://z.cash/blog/snark-explain3/) | ||
| - [Explaining SNARKs Part IV: How to make Blind Evaluation of Polynomials Verifiable](https://z.cash/blog/snark-explain4) | ||
| - [Explaining SNARKs Part V: From Computations to Polynomials](https://z.cash/blog/snark-explain5/) | ||
| - [Explaining SNARKs Part VI: The Pinocchio Protocol](https://z.cash/blog/snark-explain6) | ||
| - [Explaining SNARKs Part VII: Pairings of Elliptic Curves](https://z.cash/blog/snark-explain7) | ||
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| 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) | ||
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| Protocol descriptions: | ||
| - [zkSNARKs in a Nutshell](http://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/sapling.pdf) (very useful as detailed cheat-sheet of all cryptography used) | ||
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| ### Try | ||
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| - [libsnark (C++)](https://github.com/scipr-lab/libsnark) | ||
| - [great tutorial](https://github.com/christianlundkvist/libsnark-tutorial) | ||
| - [bellmnan (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 authors of Coda)](https://github.com/o1-labs/snarky) | ||
| - [zokrates (toolbox for zkSNARKs on Ethereum)](https://github.com/Zokrates/ZoKrates) | ||
| - [ethsnarks by HarryR (alternative toolkit for viable zk-SNARKS on Ethereum, Web, Mobile and Desktop)](https://github.com/HarryR/ethsnarks) | ||
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| ### Scaling the prover | ||
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| - [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) | ||
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| ### Multi-Party Ceremony (MPC) for Trusted Setup | ||
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| - [“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) | ||
| - [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) | ||
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| ## STARKS | ||
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|  | ||
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| 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)) | ||
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| Vitalik Buterin's blog series on STARKs: | ||
| - [Part I: Proofs with Polynomials](https://vitalik.ca/general/2017/11/09/starks_part_1.html) | ||
| - [Part II: Thank Goodness It's FRI-day](https://vitalik.ca/general/2017/11/22/starks_part_2.html) | ||
| - [Part III: Into the Weeds](https://vitalik.ca/general/2018/07/21/starks_part_3.html) | ||
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| A Hands-On Tutorial for Zero-Knowledge Proofs by Shir Peled (StarkWare): | ||
| - [Part I](http://www.shirpeled.com/2018/09/a-hands-on-tutorial-for-zero-knowledge.html) | ||
| - [Part II](http://www.shirpeled.com/2018/10/a-hands-on-tutorial-for-zero-knowledge.html) | ||
| - [Part III](http://www.shirpeled.com/2018/10/a-hands-on-tutorial-for-zero-knowledge_2.html) | ||
| - [Appendix](http://www.shirpeled.com/2018/10/a-hands-on-tutorial-for-zero-knowledge_4.html) | ||
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| Academic ressources: | ||
| - [The STARK paper](https://eprint.iacr.org/2018/046.pdf) | ||
| - [libstark implemenation](https://github.com/elibensasson/libSTARK) | ||
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| More ressources available at [starkware.co](https://www.starkware.co) | ||
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| ## Bulletproofs | ||
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| [Introduction and collection of ressources](https://crypto.stanford.edu/bulletproofs/) | ||
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| ## Social media | ||
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| Stay tuned! | ||
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| - [Awesome zero knowledge twitter list](https://twitter.com/gluk64/lists/awesome-zkp) | ||
| - [Zero-knowledge podcast](https://www.zeroknowledge.fm) |
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