From Vocdoni by Vocdoni and Lucas Menendez

At the heart of Vocdoni's mission there is to innovate secure and anonymous voting mechanisms, as we believe it's a primitive for fair and legitimate participation in many scenarios.

Voter's anonymity can be easily preserved in 1Person-1Vote scenarios, as we already offer with our SDK and UIs using zk-Snarks. However, for token-based elections, separating identities from votes is not enough because token holders have a unique balance for a token, making them easy to identify as the weight of a vote can be correlated with an address.

In this article, we'll detail our approach to resolving this issue.

Introduction

A key part of the Vocdoni stack is Census3. Census3 is a service that checks for updates to a list of tokens or other crypto assets, and maintains an updated list of holders for each registered token. This service allows users to create a census based on a token, or combining censuses using strategies, in a way compatible with Vocdoni's blockchain (Vochain).

Census3 allows creating public or anonymous-compatible censuses and publishes them on IPFS, allowing for a transparent use and public auditing. But when the election is configured to be anonymous, we must consider not only the addresses of the holders, but also their balances because depending on the token holder distribution it could be easy to identify voters.

In the context of public blockchain technology where balances are public, preserving voter anonymity on token-based elections is a big challenge. To address this, we have been considered different approaches:

The Vocdoni protocol is very flexible on how to configure and process elections. That includes weighted voting. In this type of election, not all voters wield the same power; instead, their voting power is determined by their token holdings as defined in the census.

Rounding censuses

To ensure that the balances of token-based censuses remain private, we must alter them in some way. However, any change must meet two requirements:

We explored two approaches:

Logical approach

We have developed an algorithm to meet these requirements, rounding balances to the nearest one, forming groups of at least 3 (privacyThreshold) equal balances. This process obscures individual holder's balances. The algorithm optimizes the number of members in a group, taking in account the difference between balances, to reduce the accuracy loss.

Basic steps

For example, here is the pseudocode of the core part, grouping participants (2):

Function groupAndRoundCensus Input: participants (array of Participant), privacyThreshold (integer), groupBalanceDiff (pointer to big integer) Output: array of Participant Sort participants by balance Initialize groups as an empty array of array of Participant Initialize currentGroup as an empty array of Participant For each participant in participants If currentGroup is empty Add participant to currentGroup Else Set lastParticipant to the last element in currentGroup Calculate balanceDiff as the absolute difference between participant's balance and lastParticipant's balance If the length of currentGroup is less than privacyThreshold OR balanceDiff is less than or equal to groupBalanceDiff Add participant to currentGroup Else Add currentGroup to groups Set currentGroup to a new array containing only participant If it's the last iteration Add currentGroup to groups Set roundedCensus to the result of flattening and rounding groups to the minimun balance Return roundedCensus End Function

Results accuracy

To measure accuracy, we compare the total of the adjusted balances from the census against the sum of the original balances, incorporating outliers in both calculations for consistency.

Our tests covered censuses involving 21 different tokens, showcasing various holder counts and token formats, including ERC20, ERC721, and POAP. This comprehensive testing ensures our approach is robust across different Web3 assets.

Our test results with different tokens

Initial conclusions

Our algorithm has several advantages, such as simplicity and speed. However, there's room for refinement. For example, tokens characterized by uneven distribution among holders present a challenge, as outliers not fitting into any group maintain their original balances, potentially revealing their identity.

Another problem identified is the loss of accuracy. The algorithm allows for parameter adjustments to enhance precision, and these can certainly be used to improve accuracy, but we didn't find any pattern in our test to do so. We've established parameter settings that generally perform well across various token types and distributions, so we consider this to be sufficient for now.

We've also detected potential vulnerabilities to specific attacks. For example, acquiring a certain amount of a token to manipulate the algorithm into grouping an address with others could theoretically expose that address. However, such strategies are impractical and unlikely to significantly impact election outcomes. This type of attack also requires an analysis of balance distributions, complicating its execution.

Additionally, among other possible enhancements, there is also the possibility of improving the algorithm's performance.

This is our first implementation to token-based anonymous elections. But we'll be pleased to hear about better approaches, or suggestions, to achieve anonymous voting on these and other types of elections. We warmly invite you to share them with us at chat.vocdoni.io or info[at]vocdoni.org