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awesome-zero-knowledge-proofs
A curated list of awesome things related to learning Zero-Knowledge Proofs (ZKP).
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Awesome lists are awesome, and Matter Labs, the team behind zkSync, keeps an awesome-zero-knowledge-proofs with links to all kind of resources.
This also means that, if you want to define specific thresholds for your integer variables, you'll need to add extra constraints for it. Some languages like Noir will do it for you, whereas others will require you to do it manually.
I found Circom to be the best language to start learning ZKPs, as suggested by CyberPorter. To me, Circom has the ideal level of abstraction for learning: not too high level that it abstracts away some of the quirks of ZKP, and not too low level that you get bogged down in annoying details. It also has been around for quite some time (modulo how new everything ZK is!), so you can find more documentation and samples, as well as the awesome Circom workshops from 0xparc. Last but not least, there is circomlib, a library of common building blocks for Circom.
Tornado Cash is a great learning resource on how to build a real-world zk-app with Circom circuits. I strongly recommend going through the 3-page-long white paper, as well as Gubsheep's breaking down Tornado Cash session from the 0xparc course, plus Porter's overview of the white paper.
There are multiple languages and frameworks that you can choose from for writing ZK circuits, either general purpose (like Circom) or specific to a certain platform (like Cairo). I have tried out three different languages, Circom, Halo2, and Noir, and implemented the same circuit to compare them. The circuit proves that the user knows the results of a private set of rock-paper-scissors matches, such that the total score matches a public output. The score is calculated as specified in the definition of advent of code 2022 day 2, which I used for inspiration for the problem.
Other languages and frameworks I still have to try out are Zokrates, Cairo, SnarkyJS, Gnark, and Leo. I hope to update this post as I go through them!
To me, Halo2 had the steepest learning curve by far. Not just because of having to understand how PLONKish arithmetization works to build the circuits, but mostly because I found Halo2's API quite complex and its documentation hard to find. There are also few resources for learning Halo2: the best I found were the 0xparc course which provides a few really valuable code samples, as well as the examples in the main repo. You may also want to check out awesome-halo2 for updated resources.
To me, Halo2 had the steepest learning curve by far. Not just because of having to understand how PLONKish arithmetization works to build the circuits, but mostly because I found Halo2's API quite complex and its documentation hard to find. There are also few resources for learning Halo2: the best I found were the 0xparc course which provides a few really valuable code samples, as well as the examples in the main repo. You may also want to check out awesome-halo2 for updated resources.
To me, Halo2 had the steepest learning curve by far. Not just because of having to understand how PLONKish arithmetization works to build the circuits, but mostly because I found Halo2's API quite complex and its documentation hard to find. There are also few resources for learning Halo2: the best I found were the 0xparc course which provides a few really valuable code samples, as well as the examples in the main repo. You may also want to check out awesome-halo2 for updated resources.
When starting with Halo2, keep in mind that there are two flavors of the framework out there: the vanilla one maintained by ZCash, and the fork by Ethereum's Privacy and Scaling Explorations team which uses a different polynomial commitment (KZG instead of IPA) that's more friendly for Ethereum.
As another example, you could define a circuit for proving the N-th Fibonacci number, where row i of the matrix has the values x[i-2], x[i-1], x[i]. This means you'd need three advice columns to begin with, let's call them a, b, c. Then, you'd constrain c to be equal to a + b in the same row using a gate, which requires adding a selector column for controlling it. And you'd have to set up equality constraints so that a and b are equal to b and c from the previous row. Last, in order to expose the N-th number as a public value, you'd need an instance column, constrained to equal the value of c at the last row.
Noir, built by Aztec, is the newest language of the pack and is under active development. It is distributed as nargo, a rust-based CLI, and as a set of npm packages. The npm packages releases seem to lag slightly behind the crate, which has the bleeding edge features and only got its first stable release a few days ago (early February). Both the rust crate and the npm package can be used to compile Noir programs, generate and verify proofs, and create a verifier Solidity contract.
Awesome lists are awesome, and Matter Labs, the team behind zkSync, keeps an awesome-zero-knowledge-proofs with links to all kind of resources.
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