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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. 

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. 

We analyze the Secure Remote Password (SRP) protocol for structural weaknesses using the Cryptographic Protocol Shapes Analyzer (CPSA) in the first formal analysis of SRP (specifically, Version 3). SRP is a widely deployed Password Authenticated Key Exchange (PAKE) protocol used in 1Password, iCloud Keychain, and other products. As with many PAKE protocols, two participants use knowledge of a preshared password to authenticate each other and establish a session key. SRP aims to resist dictionary attacks, not store plaintext-equivalent passwords on the server, avoid patent infringement, and avoid export controls by not using encryption. Formal analysis of SRP is challenging in part because existing tools provide no simple way to reason about its use of the mathematical expression “v + g b mod q”. Modeling v + g b as encryption, we complete an exhaustive study of all possible execution sequences of SRP. Ignoring possible algebraic attacks, this analysis detects no major structural weakness, and in particular no leakage of any secrets. We do uncover one notable weakness of SRP, which follows from its design constraints. It is possible for a malicious server to fake an authentication session with a client, without the client’s participation. This action might facilitate an escalation of privilege attack, if the client has higher privileges than does the server. We conceived of this attack before we used CPSA and confirmed it by generating corresponding execution shapes using CPSA.