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We solve a long-standing challenge to the integrity of votes cast without the supervision of a voting booth: ``{\it improper influence},'' which typically refers to any combination of vote buying and voter coercion. Our approach allows each voter, or their trusted agents (which we call ``{\it hedgehogs}''), to {\it ``nullify''} (effectively cancel) their vote in a way that is unstoppable, irrevocable, and forever unattributable to the voter. In particular, our approach enhances security of online, remote, public-sector elections, for which there is a growing need and the threat of improper influence is most acute. We introduce the new approach, give detailed cryptographic protocols, show how it can be applied to several voting settings, and describe our implementation. The protocols compose a full voting system, which we call {\it {\votexx}}, including registration, voting, nullification, and tallying---using an anonymous communication system for registration, vote casting, and other communication in the system. We demonstrate how the technique can be applied to known systems, including where ballots can be mailed to voters and voters use codes on the ballot to cast their votes online. In comparison with previous proposals, our system makes fewer assumptions and protects against a strong adversary who learns all of the voter's keys. In {\votexx}, each voter has two public-private key pairs. Without revealing their private keys, each voter registers their public keys with the election authority. Each voter may share their keys with one or more hedgehogs. During nullification, the voter, or one or more of their hedgehogs, can interact through the anonymous communication system to nullify a vote by proving knowledge of one of the voter's private keys via a zero-knowledge proof without revealing the private key. We describe a fully decentralizable implementation of {\votexx}, including its public bulletin board, which could be implemented on a blockchain. 

The conventional (election) voting systems, e.g., representative democracy, have many limitations and often fail to serve the best interest of the people in a collective decision-making process. To address this issue, the concept of liquid democracy has been emerging as an alternative decision-making model to make better use of “the wisdom of crowds”. However, there is no known cryptographically secure e-voting implementation that supports liquid democracy. In this work, we propose a new voting concept called statement voting, which can be viewed as a natural extension of the conventional voting approaches. In the statement voting, instead of defining a concrete elec- tion candidate, each voter can define a statement in his/her ballot but leave the vote “undefined” during the voting phase. During the tally phase, the (conditional) actions expressed in the statement will be carried out to determine the final vote. We initiate the study of statement voting under the Universal Composability (UC) framework, and propose several construction frameworks together with their instantiations. As an application, we show how statement voting can be used to realize a UC-secure liquid democracy voting system. We remark that our statement voting can be extended to enable more complex voting and generic ledger-based non-interactive multi-party computation. We believe that the statement voting concept opens a door for constructing a new class of e-voting schemes.