International Association
for Cryptologic Research

Decentralized e-voting enables secure and transparent elections without relying on trusted authorities, with blockchain emerging as a popular platform. It has compelling applications in Decentralized Autonomous Organizations (DAOs), where governance relies on voting with blockchain-issued tokens. Quadratic voting (QV), a mechanism that mitigates the dominance of large token holders, has been adopted by many DAO elections to enhance fairness. However, current QV systems deployed in practice publish voters' choices in plaintext with digital signatures. The open nature of all ballots comprises voter privacy, potentially affecting voters' honest participation. Prior research proposes using cryptographic techniques to encrypt QV ballots, but they work in a centralized setting, relying on a trusted group of tallying authorities to administrate an election. However, in DAO voting, there is no trusted third party.

In this paper, we propose QV Network (QV-net), the first decentralized quadratic voting scheme, in which voters do not need to trust any third party other than themselves for ballot secrecy. QV-net is self-tallying with maximal ballot secrecy. Self-tallying allows anyone to compute election results once all ballots are cast. Maximal ballot secrecy ensures that what each voter learns from QV-net is nothing more than the tally and their own ballot. We provide an open-source implementation of QV-net to demonstrate its practicality based on real-world DAO voting settings, reporting only a few milliseconds for voting and a maximum of 255 milliseconds for tallying.

The exceptional efficiency of QV-net is attributed to the design of two new Zero-Knowledge Argument of Knowledge (ZKAoK) protocols for QV ballot secrecy and integrity. Previous works generally rely on pairing-friendly curves to prove the well-formedness of an encrypted QV ballot. But they incur heavy computation and large data sizes. We tackle the challenges of appropriately formalizing and proving ZKAoK relations for QV without using these curves. Specifically, we develop a succinct ZKAoK to prove a new relation: the sum of squares of a private vector's components equals a private scalar. We also introduce the first aggregated range proof to prove that values committed under different keys fall within their respective ranges. Together, these two new zero-knowledge protocols enable us to build an efficient decentralized QV scheme and are of independent interest.