ZK Learning Resources

# ZK Learning Resources ### Curated by Outsider Analytics ###### tags: `Zero Knowledge` > Disclaimer: This work is being funded by the Ethereum Foundation PSE team. (see additional details at end) ## :rocket: Where do I start? ### :pray: Fantastic Resource Compilations (I owe a great debt to): * Technical compilation that stopped being updated in 2019: https://zkp.science/ * contributer page: https://github.com/ZKProofs/ZKProofs.github.io/graphs/contributors * Full cryptography course from Tari Labs University I only scratched the surface of: https://tlu.tarilabs.com/cryptography * Justin Martin's accessible "where do i start" resource list with good context: https://hackmd.io/24W3m1kERC-8BrI0giBRNQ?view * Tolks' Substack ZK Landscape: https://page1.substack.com/p/the-zero-knowledge-landscape?s=r * Matter Labs' "Awesome" list: https://github.com/matter-labs/awesome-zero-knowledge-proofs#readme * AtHeartEngineer's zkTech reddit with little overlap from other sources: https://www.reddit.com/r/zkTech/ ### :100: ZK Overviews: * https://docs.circom.io/background/background * An intro to ZK Snark implementation from Circom (who powers protocols like Tornado Cash) * Circom is a language which allows for the construction of ZK circuits for use in Ethereum (the witness compiles to Solidity) * While this is a bit technical, it's nice to have a more practical overview than Suduko + Where's Waldo * Zero Knowledge podcast Episode 21 (zkpe 21): intro to ZK Proofs * zkpe 34: Intro to snarks with howard Wu * https://z.cash/technology/zksnarks/ * Zcash started the applied ZK boom, and this is their ZK SNARK overview * https://www.notboring.co/p/zero-knowledge?s=r * Non-technical explanation with lots of background ### :1234: Math Background: * This will immensely help your understanding of the papers and implementations, but you can always "black box" the math side and just focus on the practical. * Lagrange interpolation: "[Secret Sharing and Erasure Coding: A Guide for the Aspiring Dropbox Decentralizer](https://blog.ethereum.org/2014/08/16/secret-sharing-erasure-coding-guide-aspiring-dropbox-decentralizer/)" * Basic math operation I found necessary to remember from high school :) * http://theory.cs.princeton.edu/complexity/book.pdf * Complexity theory is one of the fundamental ideas behind ZK tech and introduces a large amount of the notation. * Appendix A.1-3, Chapters 1, 2, 4.1-4.2, 6.1-6.4, 6.8, 7.1-7.4 * If like me this math is too complex a starting place, you may want to start on the beginning of abstract algebra. I used "A first Course in Abstract Algebra" by Fraleigh ([pdf](https://edisciplinas.usp.br/pluginfile.php/5409004/mod_resource/content/2/John%20B.%20Fraleigh%2C%20Victor%20J.%20Katz%20-%20A%20first%20course%20in%20abstract%20algebra-Addison-Wesley%20%282003%29%20%281%29.pdf)) * A couple of good companion videos: * Big O Notation: https://www.youtube.com/watch?v=0oDAlMwTrLo * P vs NP : https://www.youtube.com/watch?v=YX40hbAHx3s & https://www.youtube.com/watch?v=moPtwq_cVH8 ### :key: Cryptographic Background: * https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/ * ZK tech has its foundation in elliptic curve cryptography * This blog post does a good job of explaining the why and how elliptic curve cryptography came out of RSA and what it is. * Blockchain is not discussed in this post (don't be surprised!) * https://vitalik.ca/general/2017/01/14/exploring_ecp.html * Read this right after the above blog post to take a step for elliptic curve points in the blockchain direction * https://www.msri.org/summer_schools/931/schedules * This gets dense fast, but if you want to understand from a base level the theory behind IPs, PCPs, IOPs it's really good! * I highly recommend not starting this until you have a good understanding of the math prereqs specified in the course. (finite fields, abstract algebra, computational complexity) * This course is pretty far from practical implementation! But you will greatly increase your capacity to understand theory and important papers afterward :) * zkpe 200: Alessandro Chiesa gives a great pitch for why they built this class * Vitalik's "An approximate introduction to how zk-SNARKs are possible" * Does a great job linking the Material from MSRI summer school to real use with Fiat-Shamir heuristic. Also see in snarks theory https://vitalik.ca/general/2021/01/26/snarks.html * Justin Thaler (Georgetown)'s course and book * Huge amount of knowledge from a technical perspective * https://people.cs.georgetown.edu/jthaler/COSC544.html ### :deciduous_tree: General ZK-SNARKs Theory: * https://vitalik.ca/general/2021/01/26/snarks.html * Big picture paper I recommend reading at a few different points throughout your learning. It really ties things together well when you get into the weeds a bit too much on a specific topic * https://medium.com/@VitalikButerin/quadratic-arithmetic-programs-from-zero-to-hero-f6d558cea649 * Not Vitalik's most understandable blog post (IMHO), but the best I have seen on some of the machinery in ZK-SNARKs * This is a rare ZK paper you can actually do the math with while following along * https://medium.com/@VitalikButerin/zk-snarks-under-the-hood-b33151a013f6 * Confusing for me (TBH), but gets at the root of trusted setups and toxic waste ### :construction_worker: SNARK Constructions: * Pinocchio: Nearly Practical Verifiable Computation (2013) * https://eprint.iacr.org/2013/279.pdf * Groth16 : "On the Size of Pairing-based Non-interactive Arguments" * https://eprint.iacr.org/2016/260.pdf * Bullet Proofs * https://eprint.iacr.org/2017/1066.pdf * zkpe 40: Benedikt Bunz * Sonic * https://eprint.iacr.org/2019/099 * Plonk * https://eprint.iacr.org/2019/953 * zkpe 112: "Dive into plonk" * ["Understanding Plonk" by Vitalik](https://vitalik.ca/general/2019/09/22/plonk.html) * Marlin * https://eprint.iacr.org/2019/1047.pdf * Super Sonic * https://eprint.iacr.org/2019/1229 * zkpe 105: Alan Szepienies on Hash Functions and Supersonic SNARKs * Fractal * https://eprint.iacr.org/2019/1076 * zkpe 114: Exploring the Fractal transparent SNARK construction with Dev Ojha * Halo * https://eprint.iacr.org/2019/1021 * https://electriccoin.co/blog/halo-recursive-proof-composition-without-a-trusted-setup/ * zkpe 123: Halo with Sean Bowe and Daira Hopwood from ECC * Halo 2 * https://electriccoin.co/blog/explaining-halo-2/ * * ZEXE * https://eprint.iacr.org/2018/962.pdf * zkpe 85: Zexe: Decentralized Private Computation with Pratyush Mishra ### :stars: STARKs: * Zero-Knowledge Scalable Transparent ARguments of Knowledge * Vitalik * https://vitalik.ca/general/2017/11/09/starks_part_1.html * https://vitalik.ca/general/2017/11/22/starks_part_2.html * https://vitalik.ca/general/2018/07/21/starks_part_3.html * [Scalable, transparent, and post-quantum secure computational integrity](https://eprint.iacr.org/2018/046) * Eli Ben-Sasson, Iddo Bentov, Yinon Horesh, and Michael Riabzev * Eli Ben-Sasson presenting STARKS https://www.youtube.com/watch?v=HJ9K_o-RRSY * zkpe 59: STARKs and StarkWare with Eli & Alessandro * zkpe 96: Eli Ben-Sassson on the latest from StarkWare ### :world_map: Real World Uses * Zcash * zkpe 50: Zooko talks Zcash * Tornado Cash * zkpe 111: Mixers with Tornado.cash * https://github.com/tornadocash/docs/tree/en/circuits * Nice overview for the background of ZK circuits (GROTH16 from Circom) * https://github.com/tornadocash/docs/blob/en/circuits/core-deposit-circuit.md * zkpe 137: Trusted Setup Bonus: Tornado Cash * ZKSync (Matter Labs) * zkpe 72: zkSNARKs for Scale w/ Matter labs * zkpe 116: zkSync and Redshift with Alex Glukowski * zkpe 175: zkEVM & zkPorter with Matter Labs * Aztec * zkpe 75: Exploring Aztec with Zac Williamson * zkpe 176: ZK-zk-rollup and zk.money with Zac and Joe * Trail of Bits * Interesting Audits and security of real world ZKPs * zkpe 122: Audits & Security with Ben Perez * Dark Forest * zkpe 141: ZK & Games: Dark Forest with Brian Gu * zkpe 225: Dark Forest and 0xPARC with Gubsheep * Polygon Hermez * zkpe 194: zkEVM with Jordi & David * zkpe 219: Scaling Ethereum with Mihailo Bjelic * Polygon Miden * zkpe 210: The Road to STARKs and Miden with Bobbin Threadbare * Polygon Zero * zkpe 220: The Road to Plonky2 with Brendan and Daniel * ZoKrates * Stefan Demi's [Efficient ECC in zkSNARKs using ZoKrates](https://medium.com/zokrates/efficient-ecc-in-zksnarks-using-zokrates-bd9ae37b8186) * Good explanation for why BN128 curve is used ### :shrug: Misc Knowledge * Pedersen Commitments * https://link.springer.com/content/pdf/10.1007%2F3-540-46766-1_9.pdf#page=3 * https://crypto.stackexchange.com/questions/64437/what-is-a-pedersen-commitment * https://youtu.be/qWRUPzm3qPY (first 7 min) * Kate (Ka-tay) Commitments https://dankradfeist.de/ethereum/2020/06/16/kate-polynomial-commitments.html * Merkle tires and Patricia Tries * zkpe 57: "Merkilze this" * WASM: WebAssembly * Need to understand what this is and why it is used for witnesses. Any help appreciated! * Recursion * Scalable Zero Knowledge via Cycles of Elliptic Curves from 2014 https://eprint.iacr.org/2014/595 * zkpe 54: Digging into recursive zkSNARKs with Coda * zkpe 113: Latest recursive SNARKitecture with Izaak Meckler from 0(1) Labs * Languages/Libraries * zkpe 172: ZK languages with Alex Ozdemir * Please listen to this first! * zkpe 145: Circom & Hermez with Jordi Baylina * zkpe 41: Zokrates with Jacob Eberhardt * zkpe 126: Crypto libraries: Zcash's Zebra with Henry Valence * zkpe 169: Arkworks SNARK libraries with Pratyush Mishra * MPC * zkpe 60: Cryptography 101: Multi-Party Computations * zkpe 90: MPC systems with Nigel Smart * Randomness * True randomness is fascinating from an esoteric viewpoint * zkpe 74: Randomness and Random Beacons with Justin Drake * Trusted Setups * zkpe 133: Trusted Setup Ceremonies Explored * zkpe 137: Trusted Setup Bonus: Tornado Cash * zkpe 76: Sean Bowe on SNARKs, Trusted Setups & Elliptic Curve Cryptography * Verifiable Delay Functions * zkpe 103: Exploring VDFs with Joseph Bonneau * MiMC * https://eprint.iacr.org/2016/492.pdf * Fully Homomorphic Encryption * zkpe 124: Exploring FHE with Flavio Bergamaschi from IBM Research * baby jubjub (eliptic curves) * Zcash: https://z.cash/technology/jubjub/ ### :book: History * zkpe 90: Nigel Smart explains MPC & general history advances from the Cryptography vs. Cryptocurrancy side * zkpe 100: Great history lesson with Dan Boneh of cryptography (most useful in the beginning and end) * The OG ZKP paper from the 80s: [The Knowledge and Complexity of Interactive Proof Systems](https://people.csail.mit.edu/silvio/Selected%20Scientific%20Papers/Proof%20Systems/The_Knowledge_Complexity_Of_Interactive_Proof_Systems.pdf) * This was very academic/theoretical until about 2004 as per Nigel Smart in ZKPE 90. * If you are working through the math of abstract algebra/ complexity theory, this paper will show why it is important. It is not overly complicated * 2007 major advance from Paul Valiant [Incrementally Verifiable Computation](https://dspace.mit.edu/bitstream/handle/1721.1/38663/163581090-MIT.pdf?sequence=2) --- ### :memo: Can I contribute to/correct this page? YES! It is open editable by signed in users. Just put yourself in the credit table below :slightly_smiling_face: | Name (ANON) | Social Handles | Section Edited | Date | -------- | -------- | -------- | ------ | |Brian Wilkes| OutsiderAnalytics|The Whole Thing| 6/14/22| | | | | | If you would like to give me non-public feedback: Outsideranalytics@gmail.com --- ### :heart: If you appreciate this list and want to see it maintained! 1. Thank the Ethereum Foundation PSE team who made it possible 2. Give to Ethereum Public Works Projects on https://gitcoin.co/ (especially ZK projects) --- ### Disclaimer: This work is being funded by the Ethereum Foundation PSE team, and my crypto holdings are limited to Eth and ERC-20/721 tokens in the Ethereum/Polygon ecosystems. While this is due to my belief in the future viability/tokenomics of Ethereum, please note my inherent biases. I recognize and am truly grateful for the advances in ZK tech not associated with Ethereum, and will always strive towards the goal of impartiality!

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