3 posts tagged with "zk"

We are pleased to announce the release of an updated version of MACI - Minimal Anti-Collusion Infrastructure v1.1.1.

This new release brings a more secure product, new features, and a much needed documentation refresh. Before we dive into the updates, let's refresh your memory on what MACI is and what it was created to achieve.

Background​

MACI is an application that provides collusion resistance for on-chain voting processes. It was originally created after Vitalik's post, and has since been revisited and improved.

MACI revolves around the need for a trusted coordinator. The coordinator is in charge of setting up the system, publishing its public key, and computing the tally of the votes. Below are the main properties of MACI:

Property	Description
Collusion Resistance	No one except a trusted coordinator should be certain of the validity of a vote, reducing the effectiveness of bribery.
Receipt-freeness	No one can prove (besides to the coordinator) which way they voted.
Privacy	No one except a trusted coordinator should be able to decrypt a vote.
Uncensorability	No one — not even the trusted coordinator, should be able to censor a vote.
Unforgeability	Only the owner of a user's private key may cast a vote tied to its corresponding public key.
Non-repudiation	No one may modify or delete a vote after it is cast, although a user may cast another vote to nullify it.
Correct execution	No one, not even the trusted coordinator, should be able to produce a false tally of votes.

Since its inception, MACI has been adopted by different projects, most notably clr.fund and QFI. These projects prove how effective MACI can be, especially when integrated with applications that are otherwise prone to collusion, such as funding Public Goods.

For a more detailed description of MACI, please refer to the v1 technical introduction article.

Security Audit​

MACI was audited by HashCloak in the summer of 2022. The audit team discovered certain high risk vulnerabilities, whose fixes were the focus of the MACI team in the past months.

In more details, the audit revealed two high risk issues within the zk-SNARK circuits:

• Incomplete validation when processing messages
• Integer overflow which could have allowed users to affect a coordinator's effort of calculating the subsidy by either making it incorrect or by intercepting the calculation

Another notable security issue was the lack of initialization of the AccQueue contract. This contract is used to store messages (votes or topups) for the different polls. Without inserting a zero value hash into the merkle tree contract as the first message during initialization, a malicious user could have performed a denial of service attack on a poll. This could have resulted in the poll results taking a very long time before being tallied by the coordinator.

All of these issues have been successfully resolved, on top of fixing minor issues and general code optimizations. The updated product uses a more up to date and secure version of Solidity, and more thorough test cases to verify the correctness of the solution.

New Features​

Feature	Description
Top Up Credit	Users can now top up credits rather than having to sign up with a different MACI key
Pairwise Subsidy	Enhanced protection against collusion in quadratic funding
Coordinator Service	Sample coordinator server for easier MACI use

Top Up Credit​

Rather than requiring a user to sign up multiple times, it is now possible to top up voice credits by sending a top up message on the Poll contract. Withdrawals are not enabled as this would allow a malicious user to bribe others offline to transfer their keys.

Now, the Poll contract will hold all the funds deposited from users for the current poll. At the end of a poll, the coordinator can transfer the funds to a hardcoded address which can be used to fund public goods.

When a user deposits tokens by calling topup, they will also need to specify the stateTree index. The topup function will insert a topup message into the message queue for them. When the voting period ends, any call of topup function will be rejected. Both voting and topup messages have the same ending time, which ensures there is a well-defined ending state for each poll.

Please note that in this approach, the initial credit is still shared across multiple polls, and the actual credit an user can spend in a given poll is the following: totalCredit=initialCredit+topupCredit where the topupCredit is the voice credit amount deposited by the user during the voting period of the given pollID.

For a detailed description, please refer to this document.

Pairwise Subsidy​

Pairwise subsidy is a new way to reduce collusion in quadratic funding applications. If two contributors collude with each other, they can extract most of the public funding pool if they have enough funds.

In this post, Vitalik introduced this kind of collusion and also proposed a protocol to penalize this behavior. As a generalized solution, the more correlation between contributions, the smaller subsidy should be allocated to this project, as this reduces the risk of collusion between contributors. It should be noted that this solution assumes that an identity system is in place to prevent the same entity from registering with two different identities.

Please refer to this post for a more detailed explanation of the implementation.

Finally, please note that currently it is not possible to generate the zkeys for the subsidy circuit with with the vote options parameter larger than $5^2$. This issue is documented here and the team will focus on finding a solution to be able to support larger vote options.

Coordinator Service​

MACI now includes a sample coordinator service.

There are two roles in the coordinator service: admin (i.e. MACI coordinator) and user (i.e. a voter). The admin's responsibility is to ensure that the code remains updated and that the backend services are live. The user can then simply send HTTP requests to the backend server to interact with MACI, for instance, by signing up and publishing a message on chain.

The coordinator service has been wrapped into two docker instances: one for the backend server to accept user requests; one for the Mongodb service to store all necessary information on the current state such as smart contract addresses, zero knowledge proof keys and so on.

For further reading on coordinator services, please refer to this doc.

How to use MACI​

MACI can be used as a standalone application to carry out on-chain polls, or be implemented into new projects that can then benefit from its properties.

For use as a standalone application, a cli package is provided which allows coordinators and voters to use MACI. Please refer to this doc for details on how to use it.

To implement MACI into a project, the documentation can be used a reference, as well as reviewing how clr.fund and qf use MACI in their code.

MACI 0.x​

MACI version 0.x will be discontinued. MACI 1.x has feature parity, more robust code and newest features. Users are encouraged to use the latest version. Starting February 7, 2023, the team will focus solely on resolving issues for MACI 1.x, and will cease to provide support for version 0.x.

How to get involved​

Should you wish to get involved with MACI or simply report a bug, feel free to visit the repository and open an issue, or comment under an open issue to notify the team of your intention to work on it.

For any other enquiry, please reach out to us via the Privacy and Scaling Explorations (PSE) Discord.

References​

• MACI GitHub repository
• A technical introduction to MACI 1.0 - Kyle Charbonnet
• Minimal anti-collusion infrastructure - Vitalik
• Pairwise Subsidy
• Security Audit

Release​

Here is a link to the new release code in GitHub - v1.1.1 Release.

Introduction​

MACI, which stands for Minimal Anti-Collusion Infrastructure, is an application that allows users to have an on-chain voting process with greatly increased collusion resistance. A common problem among today’s on-chain voting processes is how easy it is to bribe voters into voting for a particular option. Oftentimes this bribery takes the form of “join our pool (vote our way) and we will give you a cut of the rewards (the bribe)”. Since all transactions on the blockchain are public, without MACI, voters can easily prove to the briber which option they voted for and therefore receive the bribe rewards.

MACI counters this by using zk-SNARKs to essentially hide how each person voted while still revealing the final vote result. User’s cannot prove which option they voted for, and therefore bribers cannot reliably trust that a user voted for their preferred option. For example, a voter can tell a briber that they are voting for option A, but in reality they voted for option B. There is no reliable way to prove which option the voter actually voted for, so the briber does not have the incentive to pay voters to vote their way.

Background​

For a general overview, the history and the importance of MACI, see Release Announcement: MACI 1.0 by Wei Jie, one of the creators. He also created a very helpful youtube video on the overview of MACI. To see the origin of the idea of MACI, see Vitalik’s research post on Minimal Anti-Collusion Infrastructure. Lastly, it is recommended to understand the basic idea behind zk-SNARKs, as these are a core component of MACI. The following articles are great resources:

• Introduction to zk-SNARKs — Consensys
• What are zk-SNARKs — Zcash
• An approximate introduction to how zk-SNARKs are possible — Vitalik
• zkSNARKs in a nutshell — Ethereum.org

This article will go over the general workflow of MACI and how it is capable of providing the following tenets (taken word for word from Wei Jie’s article):

• Collusion Resistance: No one except a trusted coordinator should be certain of the validity of a vote, reducing the effectiveness of bribery
• Receipt-freeness: No voter may prove (besides to the coordinator) which way they voted
• Privacy: No one except a trusted coordinator should be able to decrypt a vote
• Uncensorability: No one (not even the trusted coordinator) should be able to censor a vote
• Unforgeability: Only the owner of a user’s private key may cast a vote tied to its corresponding public key
• Non-repudiation: No one may modify or delete a vote after it is cast, although a user may cast another vote to nullify it
• Correct execution: No one (not even the trusted coordinator) should be able to produce a false tally of votes

System Overview​

Roles​

In the MACI workflow, there are two different roles: users (voters) and a single trusted coordinator. The users vote on the blockchain via MACI smart contracts, and the coordinator tallies up the votes and releases the final results.

The coordinators must use zk-SNARKs to prove that their final tally result is valid without releasing the vote of every individual. Therefore, even if a coordinator is corrupt, they are unable to change a user’s vote or add extra votes themselves. A corrupt coordinator can stop a vote by never publishing the results, but they can’t publish false results.

Before sending their vote on the blockchain, users encrypt their vote using a shared key that only the user and coordinator can know. This key scheme is designed so that every individual user shares a distinct key with the coordinator. This prevents any bribers from simply reading the transaction data to see which option a user voted for. The encrypted vote is now considered a “message” and the user sends this message to a MACI smart contract to be stored on-chain.

A very simplified illustration of this encryption can be seen below:

Vote Overriding and Public Key Switching​

Before a user can cast a vote, they must sign up by sending the public key they wish to use to vote to a MACI smart contract. This public key acts as their identity when voting. They can vote from any address, but their message must contain a signature from that public key. When casting an actual vote after signing up, a user will bundle a few variables — including a public key, their vote option, their vote amount, and a few others — into what is called a “command”. Then, the user signs the command with the public key they originally used to sign up. After that, the user encrypts the signature and command together so that it is now considered a message. This more complex description of how a message is constructed is illustrated below:

Users are able to override their previous vote as long as they sign their command with the previous public key. If the command is properly signed by the user’s previous public key, then the message is considered valid and the coordinator will count this as the correct vote. So, when a user provides a public key in their vote that is different than their previous public key, they may now submit a new vote signed by this new public key to override their previous vote. If the signature is not from the previous public key, the message will be marked as invalid and not counted toward the tally. Therefore, the public key can be thought of as the user’s voting username, and the signature is the voting password. If they provide the correct signature, they can submit a vote or change their public key — or both.

This feature, which I refer to as public key switching, is designed to counter the bribery attack where a user simply shows the briber their message, and then decrypts it for the briber to see which way the user voted. Public key switching allows users to change their public key and create invalid messages in favor of the bribers. The bribers have no way of telling if the user switched their public keys before sending in the vote shown to the bribers.

This can be quite confusing so here is an example:

1. Bob signs up with public key 1
2. Bob then creates a command that contains — a vote for option A and public key 2
3. Bob signs this command with public key 1, the key he used to sign up
4. Bob encrypts this command into a message and submits it to the MACI smart contracts
5. The coordinator decrypts this message, and checks to ensure that the command is signed by Bob’s previous key — public key 1. This message is valid.
6. The coordinator then records Bob’s vote for option A and updates his public key to public key 2

At this point, Bob has successfully voted for option A, and in order to override this vote must send in a new vote with a signature from public key 2. At this point, a briber now tries to get Bob to vote for option B:

1. Bob creates a command that contains — a vote for option B and public key 1
2. Bob signs this command with public key 1, encrypts the message and submits it to the MACI smart contracts
3. Bob shows the briber the decrypted message as proof of his vote for option B
4. The coordinator decrypts Bob’s message and sees that the signature does not match up with public key 2 — Bob’s previous key added in his previous message. Therefore this message is invalid and this vote is not counted in the final tally.
5. The briber has no way of knowing whether the vote was valid or invalid, and so is not incentivized to offer bribes to other users.

In order to get a good idea of how MACI works, it’s important to know how the zk-SNARKs are able to prove that the coordinator decrypted each message and tallied the votes properly. The next section gives a quick and much oversimplified overview of zk-SNARKs, although the readings listed in the introduction are much more helpful.

zk-SNARKs​

Essentially, zk-SNARKs allow users to prove they know an answer to a specific mathematical equation, without revealing what that answer is. Take the following equation for example,

X + Y = 15

I can prove that I know 2 values, X and Y that satisfy the equation without revealing what those two values are. When I create a zk-SNARK for my answer, anyone can use the SNARK (a group of numbers) and validate it against the equation above to prove that I do know a solution to that equation. The user is unable to use the SNARK to find out my answers for X and Y.

For MACI, the equation is much more complicated but can be summarized as the following equations:

encrypt(command1) = message1
encrypt(command2) = message2
encrypt(command3) = message3
…
Command1 from user1 + command2 from user2 + command3 from user3 + … = total tally result

Here, everyone is able to see the messages on the blockchain and the total tally result. Only the coordinator knows what the individual commands/votes are by decrypting the messages. So, the coordinator uses a zk-SNARK to prove they know all of the votes that:

1. Encrypt to the messages present on the blockchain
2. Sum to the tally result Users can then use the SNARK to prove that the tally result is correct, but cannot use it to prove any individual’s vote choices.

Now that the core components of MACI have been covered, it is helpful to dive deeper into the MACI workflow and specific smart contracts.

Workflow​

The general workflow process can be broken down into 4 different phases:

1. Sign Up
2. Publish Message
3. Process Messages
4. Tally Results

These phases make use of 3 main smart contracts — MACI, Poll and ​​PollProcessorAndTallyer. These contracts can be found on the MACI github page. The MACI contract is responsible for keeping track of all the user signups by recording the initial public key for each user. When a vote is going to take place, users can deploy a Poll smart contract via MACI.deployPoll().

The Poll smart contract is where users submit their messages. One MACI contract can be used for multiple polls. In other words, the users that signed up to the MACI contract can vote on multiple issues, with each issue represented by a distinct Poll contract.

Finally, the PollProcessorAndTallyer contract is used by the coordinator to prove on-chain that they are correctly tallying each vote. This process is explained in more detail in the Process Messages and Tally Results sections below.

Sign Up​

The sign up process for MACI is handled via the MACI.sol smart contract. Users need to send three pieces of information when calling MACI.signUp():

1. Public Key
2. Sign Up Gatekeeper Data
3. Initial Voice Credit Proxy Data

The public key is the original public key mentioned in above sections that the user will need to vote. As explained in earlier sections, they can change this public key later once voting starts. The user’s public key used to sign up is shared amongst every poll.

MACI allows the contract creator/owner to set a “signUpGateKeeper”. The sign up gatekeeper is meant to be the address of another smart contract that determines the rules to sign up. So, when a user calls MACI.signUp(), the function will call the sign up gatekeeper to check if this user is valid to sign up.

MACI also allows the contract creator/owner to set an “initialVoiceCreditProxy”. This represents the contract that determines how many votes a given user gets. So, when a user calls MACI.signUp(), the function will call the initial voice credit proxy to check how many votes they can spend. The user’s voice credit balance is reset to this number for every new poll.

Once MACI has checked that the user is valid and retrieved how many voice credits they have, MACI stores the following user info into the Sign Up Merkle Tree:

1. Public Key
2. Voice Credits
3. Timestamp

Publish Message​

Once it is time to vote, the MACI creator/owner will deploy a Poll smart contract. Then, users will call Poll.publishMessage() and send the following data:

1. Message
2. Encryption Key

As explained in sections above, the coordinator will need to use the encryption key in order to derive a shared key. The coordinator can then use the shared key to decrypt the message into a command, which contains the vote.

Once a user publishes their message, the Poll contract will store the message and encryption key into the Message Merkle Tree.

Process Messages​

Once the voting is done for a specific poll, the coordinator will use the PollProcessAndTallyer contract to first prove that they have correctly decrypted each message and applied them to correctly create an updated state tree. This state tree keeps an account of all the valid votes that should be counted. So, when processing the messages, the coordinator will not keep messages that are later overridden by a newer message inside the state tree. For example, if a user votes for option A, but then later sends a new message to vote for option B, the coordinator will only count the vote for option B.

The coordinator must process messages in groups so that proving on chain does not exceed the data limit. The coordinator then creates a zk-SNARK proving their state tree correctly contains only the valid messages. Once the proof is ready, the coordinator calls PollProcessorAndTallyer.processMessages(), providing a hash of the state tree and the zk-SNARK proof as an input parameters.

The PollProcessorAndTallyer contract will send the proof to a separate verifier contract. The verifier contract is specifically built to read MACI zk-SNARK proofs and tell if they are valid or not. So, if the verifier contract returns true, then everyone can see on-chain that the coordinator correctly processed that batch of messages. The coordinator repeats this process until all messages have been processed.

Tally Votes​

Finally, once all messages have been processed, the coordinator tallies the votes of the valid messages. The coordinator creates a zk-SNARK proving that the valid messages in the state tree (proved in Process Messages step) contain votes that sum to the given tally result. Then, they call PollProcessorAndTallyer.tallyVotes() with a hash of the correct tally results and the zk-SNARK proof. Similarly to the processMessages function, the tallyVotes function will send the proof to a verifier contract to ensure that it is valid.

The tallyVotes function is only successful if the verifier contract returns that the proof is valid. Therefore, once the tallyVotes function succeeds, users can trust that the coordinator has correctly tallied all of the valid votes. After this step, anyone can see the final tally results and the proof that these results are a correct result of the messages sent to the Poll contract. The users won’t be able to see how any individual voted, but will be able to trust that these votes were properly processed and counted.

Conclusion​

MACI is a huge step forward in preventing collusion for on-chain votes. While it doesn’t prevent all possibilities of collusion, it does make it much harder. MACI can already be seen to be in use by the clr.fund, which has users vote on which projects to receive funding. When the possible funding amount becomes very large, users and organizations have a large incentive to collude to receive parts of these funds. This is where MACI can truly make a difference, to protect the fairness of such important voting processes such as those at clr.fund.

The Privacy & Scaling Explorations team is proud to release version 1.0 of Minimal Anti-Collusion Infrastructure (MACI). MACI enables collusion resistance for decentralised applications, particularly voting and quadratic funding systems. This release is a major upgrade to the project and provides better developer experience and gas savings for users.

The code is in the v1 branch of the appliedzkp/macirepository and will be merged soon.

MACI 1.0 was audited by Hashcloak. All vulnerabilities found have been fixed. The audit report can be found here. We would like to thank our highly professional and responsive auditors for surfacing these issues and providing clear feedback for addressing them.

About MACI​

MACI is a set of smart contracts and zero-knowledge circuits upon which which developers can build collusion-resistant applications, such as voting systems or quadratic funding platforms. MACI per se is not a user-facing application. Rather, developers may build applications on top of it. In turn, such applications can benefit from the following properties:

• Collusion resistance: no-one, except a trusted coordinator, can be convinced of the validity of a vote, reducing the effectiveness of bribery.
• Receipt-freeness: a voter cannot prove, besides to the coordinator, which way they voted.
• Privacy: no-one, except a trusted coordinator, should be able to decrypt a vote.
• Uncensorability: no-one, not even the trusted coordinator, should be able to censor a vote.
• Unforgeability: only the owner of a user’s private key may cast a vote tied to its corresponding public key.
• Non-repudiation: no-one may modify or delete a vote after it is cast, although a user may cast another vote to nullify it.
• Correct execution: no-one, not even the trusted coordinator, should be able to produce a false tally of votes.

Practically speaking, MACI provides a set of Typescript packages, Ethereum smart contracts and zero-knowledge circuits. It inherits security and uncensorability from the underlying Ethereum blockchain, ensures unforgeability via asymmetric encryption, and achieves collusion resistance, privacy, and correct execution via zk-SNARKs.

Please note that MACI does not and will not have a token. In other words, it does not represent an investment opportunity.

MACI’s history​

MACI stems from an ethresear.ch post by Vitalik Buterin. Subsequently, the initial codebase was written in late 2019 and early 2020 by grantees with the Ethereum Foundation, namely Kendrick Tan, Koh Wei Jie, and Chih-Cheng Liang. MACI then saw developer adoption at ETHDenver in February 2020, where Auryn Macmillan and others started work on clr.fund, a protocol for the Ethereum community to allocate funds for Ethereum-based public goods.

After the event, we continued to work with clr.fund to improve MACI and integrate it with their application. clr.fund has completed seven rounds of public goods funding, the last of which saw more than US$6000 worth of contributions. At the time of writing, it is currently running an eighth round with more than US$20k in contributions.

Work on version 1.0 started in late 2020 with the goal of reducing the gas and computational requirements, as well as to improve its flexibility and usability, without compromising any of its anti-collusion, security, and trust guarantees. We also took this opportunity to keep up with new techniques, ideas, and tooling from the rapidly advancing Ethereum and zero-knowledge ecosystem.

Finally, in early 2021 we were very fortunate to bring on Cory Dickson to the team. His work on writing documentation, revamping MACI’s integration test suites, working with our auditors to fix bugs, and collaborating with external teams has been invaluable to the project.

Why is MACI important?​

It is very difficult for naive voting systems, particularly those which are integrated into smart contract platforms, to prevent collusion. For instance, if a simple Ethereum transaction represents a vote, a briber can easily examine its calldata, tell how its sender voted, and reward or punish them accordingly.

More broadly, collusion resistance is particularly important for cryptoeconomic systems. Vitalik Buterin describes the motivations behind MACI in On Collusion. He argues that systems that use cryptoeconomic incentive mechanisms to align participants’ behaviour can be vulnerable to collusion attacks, such as bribery. In another post, he elaborates:

if you can prove how you voted, selling your vote becomes very easy. Provability of votes would also enable forms of coercion where the coercer demands to see some kind of proof of voting for their preferred candidate.

To illustrate this point, consider an alleged example of collusion that occurred in round 6 of Gitcoin grants (a platform for quadratic funding software projects which contribute to public goods). In How to Attack and Defend Quadratic Funding, an author from Gitcoin highlights a tweet by a potential grant beneficiary appeared to offer 0.01 ETH in exchange for matching funds:

They explain the nature of this scheme:

While creating fake accounts to attract matching funds can be prevented by sybil resistant design, colluders can easily up their game by coordinating a group of real accounts to “mine Gitcoin matching funds” and split the “interest” among the group.

Finally, MACI is important because as crypto communities are increasingly adopting Decentralised Autonomous Organisations (DAOs) which govern through token voting. The threat of bribery attacks and other forms of collusion will only increase if left unchecked, since such attacks target a fundamental vulnerability of such systems.

What’s new?​

In this release, we rearchitected MACI’s smart contracts to allow for greater flexibility and separation of concerns. In particular, we support multiple polls within a single instance of MACI. This allows the coordinator to run and tally many elections either subsequently or concurrently.

We’ve kept the ability for developers to provide their own set of logic to gate-keep signups. For instance, application developers can write custom logic that only allows addresses which own a certain token to sign up once to MACI in order to participate in polls.

An additional upgrade we have implemented is greater capacity for signups, votes, and vote options. With MACI 1.0, a coordinator can run a round that supports more users, votes, and choices than before, even with the same hardware.

We adopted iden3’s tools for faster proof generation. Furthermore, we rewrote our zk-SNARK circuits using the latest versions of snarkjs, circom, and circomlib. We also developed additional developer tooling such as circom-helper and zkey-manager.

Finally, we significantly reduced gas costs borne by users by replacing our incremental Merkle tree contracts with a modified deposit queue mechanism. While this new mechanism achieves the same outcome, it shifts some gas costs from users to the coordinator. A comparison of approximate gas costs for user-executed operations is as follows:

Finally, we are looking forward to collaborating with other projects and supporting their development of client applications and new use cases. For instance, clr.fund team has indicated that they would like to upgrade their stack to MACI v1.0, and other projects have expressed interest in adopting MACI. We hope that through collaboration, the Ethereum community can benefit from our work, and vice versa.

Further work​

There is plenty of space for MACI to grow and we welcome new ideas. We are keen to work with developers who wish to do interesting and impactful work, especially folks who would like to learn how to build applications with zk-SNARKs and Ethereum.

Negative voting​

We thank Samuel Gosling for completing a grant for work on negative voting. This allows voters to use their voice credits to not only signal approval of a vote option, but also disapproval. Please note that the negative voting branch, while complete, is currently unaudited and therefore not yet merged into the main MACI codebase.

Anonymisation​

A suggested upgrade to MACI is to use ElGamal re-randomisation for anonymity of voters. While all votes are encrypted, currently the coordinator is able to decrypt and read them. With re-randomisation, the coordinator would not be able to tell which user took which action.

Coordinator tooling​

We are working on tooling that makes it easier for coordinators to interface with deployed contracts and manage tallies for multiple polls. This will allow users to generate proofs and query inputs and outputs from existing circuits through an easy-to-use API. We hope that this will drive more adoption of MACI and offload the need for bespoke infrastructure.

Trusted setup​

Unlike other ZKP projects, MACI does not have an official trusted setup. Instead, we hope to assist teams implementing MACI in their applications to run their own trusted setup. For instance, clr.fund recently completed a trusted setup (on a previous version of MACI) for a specific set of circuit parameters. Other teams may wish to use a different set of parameters on MACI 1.0, which calls for a different trusted setup.

Conclusion​

This release marks a step towards the hard problem of preventing collusion in decentralised voting and quadratic funding systems. We are excited to share our work and please get in touch if you are a developer and are interested in getting involved in any way.