Rapid mixing and security of Chaum’s visual electronic voting

Abstract

Recently, David Chaum proposed an electronic voting scheme that combines visual cryptography and digital processing. It was designed to meet not only mathematical security standards, but also to be accepted by voters that do not trust electronic devices. In this scheme mix-servers are used to guarantee anonymity of the votes in the counting process. The mix-servers are operated by different parties, so an evidence of their correct operation is necessary. For this purpose the protocol uses randomized partial checking of Jakobsson et al., where some randomly selected connections between the (encoded) inputs and outputs of a mix-server are revealed. This leaks some information about the ballots, even if intuitively this information cannot be used for any efficient attack. We provide a rigorous stochastic analysis of how much information is revealed by randomized partial checking in the Chaum’s protocol.We estimate how many mix-servers are necessary for a fair security level. Namely, we consider probability distribution of the permutations linking the encoded votes with the decoded votes given the information revealed by randomized partial checking. We show that the variation distance between this distribution and the uniform distribution is O(1) already for a constant number of mix-servers (n is the number of voters). This means that a constant number of trustees in the Chaum’s protocol is enough to obtain provable security. The analysis also shows that certain details of the Chaum’s protocol can be simplified without lowering security level.