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A Homomorphic LWE Based E-voting Scheme

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Post-Quantum Cryptography (PQCrypto 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9606))

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Abstract

In this paper we present a new post-quantum electronic-voting protocol. Our construction is based on LWE fully homomorphic encryption and the protocol is inspired by existing e-voting schemes, in particular Helios. The strengths of our scheme are its simplicity and transparency, since it relies on public homomorphic operations. Furthermore, the use of lattice-based primitives greatly simplifies the proofs of correctness, privacy and verifiability, as no zero-knowledge proof are needed to prove the validity of individual ballots or the correctness of the final election result. The security of our scheme is based on classical SIS/LWE assumptions, which are asymptotically as hard as worst-case lattice problems and relies on the random oracle heuristic. We also propose a new procedure to distribute the decryption task, where each trustee provides an independent proof of correct decryption in the form of a publicly verifiable ciphertext trapdoor. In particular, our protocol requires only two trustees, unlike classical proposals using threshold decryption via Shamir’s secret sharing.

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Notes

  1. 1.

    Probabilistic Polynomial Timing.

  2. 2.

    Technically speaking, the smoothing parameter of the real lattice \(G+\mathbb {Z}^n\) must be smaller than \(\alpha {\slash }\sqrt{2n}\), as implied by [14] or [6].

  3. 3.

    The revote policy consists in accepting the last vote sent for \(\mathsf {upk}\): \(\mathsf {BB}\) accepts to overwrite a ballot for \(\mathsf {upk}\) iff the new version number is strictly larger than the previous one.

  4. 4.

    the \(v_i\) exists and is unique, but \(b_i\) might have been generated without its knowledge, or more generally, without calling the \(\mathsf {Vote}\) procedure.

  5. 5.

    This works well in the random oracle model as in Assumption 3.5. Getting it in the standard model remains open.

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Acknowledgments

This work has been supported in part Fonds Unique Interministériel (FUI)through the CRYPTOCOMP project and the EIT Digital project HC@WORKS.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035, Versailles, France

    Ilaria Chillotti & Nicolas Gama

  2. Inpher, Lausanne, Switzerland

    Nicolas Gama

  3. Gemalto, 6 rue de la Verrerie, 92190, Meudon, France

    Mariya Georgieva

  4. CEA LIST, Point Courrier 172, 91191, Gif-sur-Yvette Cedex, France

    Malika Izabachène

Authors
  1. Ilaria Chillotti
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  2. Nicolas Gama
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  3. Mariya Georgieva
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  4. Malika Izabachène
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Corresponding author

Correspondence to Ilaria Chillotti .

Editor information

Editors and Affiliations

  1. Kyushu University, Fukuoka, Japan

    Tsuyoshi Takagi

Appendix

Appendix

Assuming a medium-scale election with \(L\approx 2000\) voters, the main partial keys should allow a \(1{\slash }L^{1.5}\approx 2^{-17}\) noise parameter. Taking into account the overhead for publicly verifiable ciphertext trapdoors and bootstrapping key, the overall scheme can easily be instantiated with at most 2000-bit secrets.

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Chillotti, I., Gama, N., Georgieva, M., Izabachène, M. (2016). A Homomorphic LWE Based E-voting Scheme. In: Takagi, T. (eds) Post-Quantum Cryptography. PQCrypto 2016. Lecture Notes in Computer Science(), vol 9606. Springer, Cham. https://doi.org/10.1007/978-3-319-29360-8_16

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  • DOI: https://doi.org/10.1007/978-3-319-29360-8_16

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