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Receipt-free remote electronic elections with everlasting privacy

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Abstract

We present a new cryptographic voting protocol for remote electronic voting that offers three of the most challenging features of such protocols: verifiability, everlasting privacy, and receipt-freeness. Trusted authorities and computational assumptions are only needed during vote casting and tallying to prevent the creation of invalid ballots and to achieve receipt-freeness and fairness, but not to guarantee vote privacy. The implementation of everlasting privacy is based on perfectly hiding commitments and non-interactive zero-knowledge proofs, whereas receipt-freeness is realized with mix networks and homomorphic tallying.

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Notes

  1. To ensure that generators are independent, they need to be generated in some publicly reproducible way, for example by deriving them from a common reference string.

  2. We are aware that requiring a secure platform is a strong assumption. We do not explicitly address this problem in this paper, but our protocol allows voters at least to detect a compromised platform as long as they can read the bulletin board in a secure way.

  3. To ensure that u has been computed from fresh values (α,β,γ), the voter could be asked to prove knowledge of (α,β,γ) by computing \(\mathit {NIZKP}[(\alpha ,\beta ,\gamma ):u = h_{1}^{\alpha }h_{2}^{\beta }h_{3}^{\gamma }]\). As this is not an essential step for our protocol, we omit it in our presentation.

  4. At first sight, it may appear that π 2 and π 3 are very similar proofs, but a subtle difference disallows π 2 to be implemented as a standard preimage proof. The subtlety lies in the fact that u and \(\hat {u}\) are both elements of \(\mathbb {G}_{q}\), but to use u as input of \(\text {com}_{p}:\mathbb {Z}_{p}\times \mathbb {Z}_{p}\rightarrow \mathcal {G}_{p}\), it needs to be interpreted as an element of \(\mathbb {Z}_{p}\). As a consequence, com p is not a group homomorphism with respect to (α,β,γ), i.e., the preconditions for constructing a preimage proof are not satisfied.

  5. The bulletin board could also accept multiple copies of the same ballot, which then need to be eliminated in the tallying phase. But this makes preventing replay and board flooding attacks more complicated.

  6. Shuffling and decrypting a list of ciphertexts can be performed in a single serial process [38]. This is an optional implementation variant of our protocol, which we do not pursue here.

  7. By mixing up list and set operations in one expression, we slightly abuse standard mathematical notation.

  8. Some lists are implicitly given: E F (follows from B), \(\mathbf {E}^{\prime }\) (follows from \(\mathbf {EF}^{\prime }\)), F H (follows from H and \(\mathbf {EF}^{\prime }\)), and \(\mathbf {V}^{\prime }\) (follows from V). As such, they need not to be published, but we include them for improved clarity.

  9. In case x is shared among multiple authorities, the literal y = h x in π 4 can be replaced by a disjunction \(\bigvee _{\!j} (y_{j}=h^{x_{i}})\), where x i is a single private key share of an individual trusted authority and y j are corresponding public values of all trusted authorities. In this way, null votes can be generated individually by a single trusted authority.

  10. An additive vote encoding capable of representing all possible election results is necessary for this.

  11. The security parameter K determines the soundness of the proof. We adopt the recommendation of K≥80 from [4].

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Acknowledgments

Research supported by the Swiss National Science Foundation (project No. 200021L_140650).

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Authors and Affiliations

  1. Bern University of Applied Sciences, 2501, Biel, Switzerland

    Philipp Locher & Rolf Haenni

  2. University of Fribourg, 1700, Fribourg, Switzerland

    Philipp Locher

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Correspondence to Philipp Locher.

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Locher, P., Haenni, R. Receipt-free remote electronic elections with everlasting privacy. Ann. Telecommun. 71, 323–336 (2016). https://doi.org/10.1007/s12243-016-0519-6

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