Many voter-verifiable, coercion-resistant schemes have been proposed, but even the most carefully designed systems necessarily leak information via the announced result. In corner cases, this may be problematic. For example, if all the votes go to one candidate then all vote privacy evaporates. The mere possibility of candidates getting no or few votes could have implications for security in practice: if a coercer demands that a voter cast a vote for such an unpopular candidate, then the voter may feel obliged to obey, even if she is confident that the voting system satisfies the standard coercion resistance definitions. With complex ballots, there may also be a danger of "Italian" style (aka "signature") attacks: the coercer demands the voter cast a ballot with a specific, identifying pattern. Here we propose an approach to tallying end-to-end verifiable schemes that avoids revealing all the votes but still achieves whatever confidence level in the announced result is desired. Now a coerced voter can claim that the required vote must be amongst those that remained shrouded. Our approach is based on the well-established notion of Risk-Limiting Audits, but here applied to the tally rather than to the audit. We show that this approach counters coercion threats arising in extreme tallies and "Italian" attacks. We illustrate our approach by applying it to the Selene scheme, and we extend the approach to Risk-Limiting Verification, where not all vote trackers are revealed, thereby enhancing the coercion mitigation properties of Selene.
A number of papers @cite_3 @cite_19 @cite_20 @cite_7 try to achieve tally hiding, either by only calculating the winner(s), or via multi-party computation and other cryptographic means. An idea closer to RLTs is that of Random Sample Voting (RSV) by Chaum @cite_6 . A scheme that seeks to implement RSV in a fully verifiable fashion is Alethea @cite_13 . RSV typically samples a small and predetermined number of voters, regardless of the margins. In contrast, RLTs adjust the sample size to obtain the desired level of confidence in the reported outcome.
@cite_7 @cite_3 @cite_6 @cite_19 @cite_13 @cite_20
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There are many sources of error in counting votes: the apparent winner might not be the rightful winner. Hand tallies of the votes in a random sample of precincts can be used to test the hypothesis that a full manual recount would find a different outcome. This paper develops a conservative sequential test based on the vote-counting errors found in a hand tally of a simple or stratified random sample of precincts. The procedure includes a natural escalation: If the hypothesis that the apparent outcome is incorrect is not rejected at stage s, more precincts are audited. Eventually, either the hypothesis is rejected-and the apparent outcome is confirmed-or all precincts have been audited and the true outcome is known. The test uses a priori bounds on the overstatement of the margin that could result from error in each precinct. Such bounds can be derived from the reported counts in each precinct and upper hounds on the number of votes cast in each precinct. The test allows errors in different precincts to be treated differently to reflect voting technology or precinct sizes. It is not optimal, but it is conservative: the chance of erroneously confirming the outcome of a contest if a full manual recount would show a different outcome is no larger than the nominal significance level. The approach also gives a conservative P-value for the hypothesis that a full manual recount would find a different outcome, given the errors found in a fixed size sample. This is illustrated with two contests from November, 2006: the U.S. Senate race in Minnesota and a school hoard race for the Sausalito Marin City School District in California, a small contest in which voters could vote for up to three candidates. In random sample voting, only a randomly chosen subset of all eligible voters are selected to vote. This poses new security challenges for the voting protocol used. In particular, one must ensure that the chosen voters were randomly selected while preserving their anonymity. Moreover, the small number of selected voters leaves little room for error and only a few manipulations of the votes may significantly change the outcome. We propose Alethea, the first random sample voting protocol that satisfies end-to-end verifiability and receipt-freeness. Our protocol makes explicit the distinction between human voters and their devices. This allows for more fine-grained statements about the required capabilities and trust assumptions of each agent than is possible in previous work. We define new security properties related to the randomness and anonymity of the sample group and the probability of undetected manipulations. We prove correctness of the protocol and its properties both using traditional paper and pen proofs and with tool support. We present a new paper-based voting method with interesting security properties. The attempt here is to see if one can achieve the same security properties of recently proposed cryptographic voting protocols, but without using any cryptography, using only paper ballots. We partially succeed. (Initially, I thought the proposal accomplished this goal, but several readers discovered a vote-buying attack (see Section 4.4) that appears to be rather difficult to fix without making the resulting system much less usable in practice. Currently, this paper should thus be viewed more as an academic proposal than a practical proposal. Perhaps some variation on these ideas in this paper might still turn out to be of practical use. The “OneBallot with Exchanged Receipts” system sketched at the end of Section 5.3.1, looks particularly promising at the moment. . . ) The principles of ThreeBallot are simple and easy to understand. In this proposal, not only can each voter verify that her vote is recorded as she intended, but she gets a “receipt” that she can take home that can be used later to verify that her vote is actually included in the final tally. Her receipt, however, does not allow her to prove to anyone else how she voted. In this “ThreeBallot” voting system, each voter casts three paper ballots, with certain restrictions on how they may be filled out, so the tallying works. These paper ballots are of course “voter-verifiable.” All ballots cast are scanned and published on a web site, so anyone may correctly compute the election result. A voter receives a copy of one of her ballots as her “receipt”, which she may take home. Only the voter knows which ballot she copied for her receipt. The voter is unable to use her receipt to prove how she voted or to sell her vote, as the receipt doesn’t reveal how she voted. A voter can check that the web site contains a ballot ∗The latest version of this paper can always be found at http: theory.csail.mit.edu rivest Rivest-TheThreeBallotVotingSystem.pdf matching her receipt. Deletion or modification of ballots is thus detectable; so the integrity of the election is verifiable. We present a mathematical construct which provides a cryptographic protocol to verifiably shuffle a sequence of k modular integers, and discuss its application to secure, universally verifiable, multi-authority election schemes. The output of the shuffle operation is another sequence of k modular integers, each of which is the same secret power of a corresponding input element, but the order of elements in the output is kept secret. Though it is a trivial matter for the "shuffler" (who chooses the permutation of the elements to be applied) to compute the output from the input, the construction is important because it provides a linear size proof of correctness for the output sequence (i.e. a proof that it is of the form claimed) that can be checked by an arbitrary verifiers. The complexity of the protocol improves on that of Furukawa-Sako[16] both measured by number of exponentiations and by overall size.The protocol is shown to be honest-verifier zeroknowledge in a special case, and is computational zeroknowledge in general. On the way to the final result, we also construct a generalization of the well known Chaum-Pedersen protocol for knowledge of discrete logarithm equality [10], [7]. In fact, the generalization specializes exactly to the Chaum-Pedersen protocol in the case k = 2. This result may be of interest on its own.An application to electronic voting is given that matches the features of the best current protocols with significant efficiency improvements. An alternative application to electronic voting is also given that introduces an entirely new paradigm for achieving Universally Verifiable elections.