Secure and Verifiable Electronic Elections at NTNU

Abstract

This thesis describes an electronic voting system based on Damgaa rd, Jurik and Nielsen's generalization of Paillier's probabilistic public key system. A threshold variant of this homomorphic cryptosystem is used to provide universally verifiable elections, where zero-knowledge proofs are used for proving correctness of votes. Using this cryptosystem, an electronic voting system that supports voting for 1 out of $L$ candidates is described. Two types of encoding may be used to prove the validity of the votes. The number of proofs needed using normal encoding is linear in $L$, while the number of proofs needed using binary encoding is logarithmic in $L$. It is shown how to extend the system to allow casting a vote for $t$ out of $L$ candidates. This method may easily be used to carry out elections with weighted votes without any added complexity to the system. The system is shown to satisfy the requirements for elections at The Norwegian University of Science and Technology (NTNU). A fully functional implementation of the electronic voting system as a distributed system, using Java Remote Method Invocation, is presented. The implementation is used to analyze the feasibility of using this voting system for future elections at NTNU. The implementation is tested using various keylengths and various election parameters. With a keylength of 1024 bits, the simulated time for verification of complex elections is small enough to be considered universally verifiable.