Non-interactive Zero-Knowledge Arguments for Voting

• Published in: Applied Cryptography and Network Security pp. 467 - 482
• Main Author: Groth, Jens
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Computer science; control theory; systems; Cryptography; Exact sciences and technology; Information, signal and communications theory; Memory and file management (including protection and security); Memory organisation. Data processing; Signal and communications theory; Software; Telecommunications and information theory; Probabilistic approach; Voting; Heuristic method; Encryption; Zero knowledge protocol; Distributed system; Cryptography; Oracle; Modeling; Computer security
• ISBN: 3540262237; 9783540262237
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11496137_32

In voting based on homomorphic threshold encryption, the voter encrypts his vote and sends it in to the authorities that tally the votes. If voters can send in arbitrary plaintexts then they can cheat. It is therefore important that they attach an argument of knowledge of the plaintext being a correctly formed vote. Typically, these arguments are honest verifier zero-knowledge arguments that are made non-interactive using the Fiat-Shamir heuristic. Security is argued in the random oracle model. The simplest case is where each voter has a single vote to cast. Practical solutions have already been suggested for the single vote case. However, as we shall see homomorphic threshold encryption can be used for a variety of elections, in particular there are many cases where voters can cast multiple votes at once. In these cases, it remains important to bring down the cost of the NIZK argument. We improve on state of the art in the case of limited votes, where each voter can vote a small number of times. We also improve on the state of the art in shareholder elections, where each voter may have a large number of votes to spend. Moreover, we improve on the state of the art in Borda voting. Finally, we suggest a NIZK argument for correctness of an approval vote. To the best of our knowledge, approval voting has not been considered before in the cryptographic literature.