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We solve a long-standing challenge to the integrity of votes cast without the supervision of a voting booth: ``improper influence,'' which we define as any combination of vote buying and voter coercion. In comparison with previous proposals, our system is the first in the literature to protect against a strong adversary who learns all of the voter's keys---we call this property ``extreme coercion resistance.'' Our approach allows each voter, or their trusted agents (which we call ``hedgehogs''), to ``nullify'' (effectively cancel) their vote in a way that is unstoppable and irrevocable, and such that the nullification action is forever unattributable to that voter or their hedgehog(s). We demonstrate the security of VoteXX in the {universal composability} model. Additionally we provide concrete implementations of sub-protocols---including inalienable authentication, decentralized bulletin boards, and anonymous communication channels---that are usually left as abstract assumptions in the literature. As in many other coercion-resistant systems, voters are authorized to vote with public-private keys. Each voter registers their public keys with the Election Authority (EA) in a way that convinces the EA that the voter has complete knowledge of their private keys. Voters concerned about losing their private keys can themselves, or by delegating to one or more hedgehog(s), monitor the bulletin board for malicious ballots cast with their keys, and can act to nullify these ballots in a privacy-preserving manner with zero-knowledge proofs. In comparison with previous proposals, our system makes fewer assumptions and protects against a stronger adversary. For example, votexx makes none of the following assumptions made by previous systems: the voter must complete registration before being coerced; the election will not close before the voter can cast a ballot after coercion; the voter needs to generate a fake password to evade coercion; and the voter knows an honest Election Authority official. 

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. 

We present and analyze UDM, a new protocol for user discovery in anonymous communication systems that minimizes the information disclosed to the system and users. Unlike existing systems, including those based on private set intersection, UDM learns nothing about the contact lists and social graphs of the users, is not vulnerable to off-line dictionary attacks that expose contact lists, does not reveal platform identifiers to users without the owner’s explicit permission, and enjoys low computation and communication complexity. UDM solves the following user-discovery problem. User Alice wishes to communicate with Bob over an anonymous communication system, such as cMix or Tor. Initially, each party knows each other’s public contact identifier (e.g., email address or phone number), but neither knows the other’s private platform identifier in the communication system. If both parties wish to communicate with each other, UDM enables them to establish a shared key and learn each other’s private platform identifier. UDM uses an untrusted user-discovery system, which processes and stores only public information, hashed values, or values encrypted with keys it does not know. Therefore, UDM cannot learn any information about the social graphs of its users. Using the anonymous communication system, each pair of users who wish to communicate with each other uploads to the user-discovery system their private platform identifier, encrypted with their shared key. Indexing their request by a truncated cryptographic hash of their shared key, each user can then download each other’s encrypted private platform identifier.